ADAPTIVELY FILTERING TRANS-IMPEDANCE AMPLIFIER FOR RF CURRENT PASSIVE MIXERS

Transcription

1 ADAPTIVELY FILTERING TRANS-IMPEDANCE AMPLIFIER FOR RF CURRENT PASSIVE MIXERS by Tian Ya Liu A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Graduate Department of Electrical and Computer Engineering University of Toronto Copyright 2016 by Tian Ya Liu

2 Abstract Adaptively Filtering Trans-Impedance Amplifier for RF Current Passive Mixers Tian Ya Liu Master of Applied Science Graduate Department of Electrical and Computer Engineering University of Toronto 2016 Current Passive Mixers represent the state of the art for the signal down-conversion in wireless receivers. In such kind of structures, noise, distortion, and losses are strictly correlated to the stage following the mixer. This thesis proposed a trans-impedance amplifier (TIA) to sense the down-converted current with a new topology that adaptively filters the out-of-band interferers as a function of input current magnitude with a class-ab transconductor in the feedback network. The prototype is implemented in IBM 0.13μm CMOS technology, and shows low input impedance with a high-pass shaped noise and distortion profile. The filter cut-off frequency is reconfigurable between 2.8MHz and 12MHz. The prototype consumes 1.92mW of power from a 1.2V supply and the active die area is 0.45mm 2. It achieves out-of-band SFDR between 86.8dB and 75.1dB, with the FOM varies between 182 db(j -1 ) and 176 db(j -1 ). ii

3 Acknowledgments First and foremost, I would like to thank my supervisor Professor Antonio Liscidini for providing me with detailed guidance and support. I am glad to be his first M.A.Sc student at University of Toronto. His technical advices have been invaluable and memorable during the past two years. I would also like to thank the committee members, Professor Liscidini, Professor Genov, Professor Sheikholeslami and Professor Prodic for their time, valuable feedbacks, and comments. Second, I would like to thank Jason (Chuanwei) Li for providing help with all the CAD tools and layout techniques during my second year, and all the discussions we had. I would also like to thank all the colleagues in BA5000 for all the interesting conversations and interactions we had. Finally, I would like to thank my parents for all the support and understandings through the duration of my master study and my life. iii

4 Table of Contents Acknowledgments... iii List of Tables... vii List of Figures... viii List of Acronyms... xi Chapter Introduction Motivation Objective Thesis Outline... 2 Chapter Trans-Impedance Amplifier Overview RF Receiver Basics and Specifications State-of-the-Art TIA Structure Overview TIA Input Impedance and Comparison TIA Noise and Comparison Summary Chapter Proposed Trans-Impedance Amplifier Structure and Transfer Function Finite Trans-Conductance and Gain Bandwidth Product Reconfigurable TIA Filter Input Impedance Spurious-Free Dynamic Range iv

5 3.3.1 Noise Transfer Functions and Analysis Linearity and Intermodulation Phenomena Stability Analysis Adaptive Filtering Response Summary Chapter System and Circuit Design Operational Amplifier in Feed-Forward Path Operational Trans-conductance Amplifier in Feedback Network Reconfigurable TIA with MOS switches and Capacitor banks Stability Analysis Simulation Results Summary Chapter Measurement Results Test Setup Device Under Test Printed Circuit Board Equipment Setup TIA Measurement Results and Comparison Filter Transfer Function Input Impedance Two-Tone Intermodulation Test Noise Measurement Performance Summary and Comparison Chapter v

6 Conclusion Summary Future Work Bibliography vi

7 List of Tables 2.1 Design Specifications and Circuit parameters for Tow-Thomas Filter Design Specifications and Circuit parameters for Rauch Filter Summary of State-of-the-Art TIA Topologies and Comparison Design Specifications and Circuit parameters for the Reconfigurable TIA Summarized Stability Simulation Results Summary of Simulation Results Summary of Measurement Results Comparison with other published works...73 vii

8 List of Figures 2.1 The Zero-IF Receiver Architecture WCDMA Out-of-band Blocker Test State-of-the-Art Filtering TIA topologie Filtering TIA: Single Pole Virtual Ground with Large Grounded Capacitance Filtering TIA: Two Real Poles with Switchable Compensation Filtering TIA: Tow-Thomas Biquad Filter Filtering TIA: Current Driven Rauch Biquad Filter Bode Plot - Input Impedance of Tow-Thomas Filter with varying GBP Bode Plot-Input Impedance of Rauch Filter with varying GBP Tow-Thomas Filter with Noise Sources Tow-Thomas Filter Output Noise Transfer Function with Each Noise Source Rauch Filter with Noise Sources Rauch Filter Output Noise Transfer Function with Each Noise Source Proposed Filtering TIA with zeros in the feedback network Original Filtering TIA with active feedback network Bode plot - Transfer function of TIA current and Interferer current over Input current Quality Factor as a Function of varying Trans-Conductance gm Bode plot Transfer Function and Phase Response of the TIA with Increasing Trans- Conductance gm Bode plot Transfer Function and Phase Response of TIA With Real Parameters Proposed Filtering TIA with Reconfigurable Cut-off Frequency Bode Plot Transfer Function of Amplitude and Phase Response with Re-configurable Cutoff Frequency Bode Plot Input Impedance Transfer Function of Proposed TIA Filter with Varying Parameters...34 viii

9 3.10 Bode Plot Input Impedance of Proposed TIA Filter with Reconfiguring Bandwidth and Scaling Options Proposed TIA Filter with Noise Sources Proposed TIA Filter Output Noise Transfer Function with All Noise Source Proposed TIA Filter Intermodulation Product Phenomena TIA Loop Gain Analysis All Breaking Points TIA Loop Gain Analysis Overall Loop Gain Bode Plot Bode Plot Adaptive Transfer Function Sketch of Proposed TIA with Increasing Interferer Power (Theoretical) Conventional TIA Small Signal Model of the Two-Stage Miller Compensated Op-Amp Two-Stage Miller Compensated Op-Amp for the Proposed TIA Common Mode Feedback Amplifier for Two-Stage OP-AMP Simplified Scheme for CMOS Trans-conductor Proposed Operational Trans-conductance Amplifier with Bias in Class-A or Class-AB OTA Output Voltages and Drain Currents with Different Input Current at 50MHz Common Mode Feedback Amplifiers for OTA Reconfigurable TIA with Switch and Capacitor Banks Reconfigurable TIA Top Level Schematic Bode Plot Loop Gain of the TIA Main Loop Bode Plot Loop Gain of the Feed-forward Op-Amp Bode Plot Loop Gain of the Op-Amp Common Mode Feedback Bode Plot Loop Gain of the OTA Common Mode Feedback Bode Plot - Simulated Reconfigurable TIA Signal Transfer Functions Bode Plot - Simulated TIA Adaptive Transfer Function with Different Input Signal (cut-off frequency at 3.1MHz) Bode Plot- Simulated Reconfigurable TIA Input Impedance Transfer Functions...60 ix

10 4.18 Simulated Output Noise Comparison with State-of-the-Art Designs (f 4.19 Simulated Output Noise Reconfigurable TIA with High-pass Noise Shaping Two Tone Out-of-Band Linearity and 19.5MHz for Lowest Band Configuration Two Tone Out-of-Band Linearity and 95MHz for Highest Band Configuration Chip Die Photo Printed Circuit Board Block Diagram Printed Circuit Boards Graphic User Interface for Measurement with LABVIEW Measured Transfer Function of the Reconfigurable TIA Measured Adaptive Transfer Function of the TIA (Lowest Bandwidth) Measured Input Impedance of the Reconfigurable TIA Measured Adaptive Input Impedance in Ohms (Lowest Bandwidth) Two Tone Tests: Output IM 3 In-band High-pass Shaping (Lowest bandwidth) IM 3 Product Bends for Large Input Signal dB Compressing Point with Large Out-of-Band Input Signal Measured Output Noise Spectrum for Lowest Bandwidth Measured Output Noise Spectrum for Highest Bandwidth...75 x

11 List of Acronyms CAD Computer Aided Design CMOS Complementary metal oxide semiconductor DR Dynamic Range DUT Device Under Test FOM Figure of Merit FPGA Field-Programmable Gate Array GBP Gain Bandwidth Product GUI Graphical User Interface IIP3 Third Order Input Intercept Point IM Intermodulation LNA Low Noise Amplifier LTE Long-Term Evolution NMOS N-Channel MOSFET OP-AMP Operational Amplifier OTA Operational Trans-conductance Amplifier PCB Printed Circuit Board PMOS P-Channel MOSFET PVT Process Voltage Temperature xi

12 Q Factor Quality Factor RF Radio Frequency SFDR Spurious-Free Dynamic Range SMA SubMiniature version A TIA Trans-Impedance Amplifier USB Universal Serial Bus WCDMA Wideband Code Division Multiple Access xii

13 CHAPTER 1. INTRODUCTION 1 Chapter 1 Introduction 1.1 Motivation Nowadays, current passive mixers represent the state of the art for the signal down-conversion in wireless receivers. In such kind of structures, noise, distortion and losses are strictly correlated to the stage following the mixer. The most common solution adopted to sense the down-converted current is a trans-impedance amplifier (TIA) in shunt with a ground capacitance that assures low input impedance when the loop-gain of the amplifier decreases. Low input impedance is necessary to have a small voltage swing at the output of the mixer (typically a few hundred mv) to minimize the modulation of the switch resistance and with it the distortion produced during the down-conversion. For the TIA to handle a small signal and a large out-of-band interferer, the spurious-free dynamic range (SFDR) requirement becomes very challenging. A ground input capacitance can be also used to filter the majority of the out-of-band interferers by transforming the TIA into a filter [1],[2]. This reduces the dynamic range required by the TIA and its power consumption. However, this advantage is often paid in terms of area and power since the limited voltage swing tolerable at the input of the TIA demands a large capacitor to absorb the downconverted interferers and higher power consumption in the amplifier to achieve a better linearity. The idea originally proposed in [3] places an active feedback network only to improve out-ofband large-signal attenuation and 1dB compression point. A TIA filter typically occupies 20%- 30% of the analog frond end in the receivers. This TIA in [3] consumes high power and uses a large amount of capacitances (area) only for tolerating large input signals while keeping the input voltage swing small. The idea in [3] is re-used in this thesis to target the implementation of a TIA filter that breaks off these trade-offs and occupies small area with lower total capacitance; provides low input impedance, and high SFDR with lower power consumption; utilizes the characteristics of the structure to achieve an adaptive filtering response as a function of out-ofband input current magnitude; and finally be able to reconfigure the filter cut-off frequency to work between WCDMA standard and LTE standard.

14 CHAPTER 1. INTRODUCTION Objective The main objectives of this thesis are as follows: 1. Provide a background of existing TIAs for wireless applications and review their architectures in terms of transfer functions, input impedance, noise and linearity. 2. Propose a low power TIA with small area that provides low input impedance, adaptive filtering profile, high SFDR and Figure of Merit (FOM) among all the other existing designs. 3. Show theoretical equations, circuit-level simulations, implementations, and prototype measurement results to validate the design. 1.3 Thesis Outline Chapter 2. Trans-Impedance Amplifier Overview: This chapter describes the existing solutions of TIAs and compares with the same specifications as the proposed design in terms of transfer function, input impedance, noise and linearity. Chapter 3. Proposed Trans-Impedance Amplifier: A new TIA topology is introduced by the proposed design and the key properties of the filter are studied in detail, including transfer functions, input impedance, Spurious-Free Dynamic Range, and re-configurability. The design parameters and sizes of the capacitor and resistors are summarized at the end of the chapter. Chapter 4. System and Circuit Design: This chapter describes each individual elements of the TIA filter; Transistor level design choices are explained in detail. The simulation results are also shown to verify the design including transfer function, input impedance, linearity, noise, power, and re-configurability. Chapter 5. Measurement Results: This chapter shows the measurement results of the TIA prototype described in Chapter 4. The results are presented in graphs and tables to compare with other state-of-the-art designs. Chapter 6. Conclusion: This chapter summarizes the thesis and future work is discussed.

15 CHAPTER 2. TRANS-IMPEDANCE AMPLIFIEROVERVIEW 3 Chapter 2 Trans-Impedance Amplifier Overview 2.1 RF Receiver Basics and Specifications Figure 2.1 shows the common architecture of the zero-if receivers. In this architecture, RF signal is directly translated to baseband, which is done by making the local osillator (LO) frequency equal to the RF signal. Current passive mixer is often used for signal down-conversion followed by a low-pass filtering trans-impedance amplifier in baseband. Figure 2.1: The Zero-IF receiver architecture The channel bandwidth is folded in half when it is converted down to baseband. The standard 3G Wideband Code Division Multiple Access (WCDMA) channel length is 3.84MHz in the RF receiver requirements [4], that makes 1.92MHz for the baseband section which contains the lowpass filter and defines the minimum filter bandwidth. For 4G Long-Term Evolution (LTE), the most common channel bandwidths are 5MHz, 10MHz, and 20MHz, which makes a maximum of 10MHz for the baseband filter. Figure 2.2 shows the blocker test for the WCDMA baseband section. The maximum out-of-band input referred power in the figure is -15dBm at 85MHz offset. Considering a total transconductance of 40mS for typical LNA and mixer down-conversion [2], the maximum input current amplitude for the baseband filter is approximately 2.24mA (a few ma).

16 CHAPTER 2. TRANS-IMPEDANCE AMPLIFIEROVERVIEW 4 Figure 2.2: WCDMA Out-of-band blocker test 2.2 State-of-the-Art TIA Structure Overview Filtering TIA topologies shown in Figure 2.3 a-d) are the most common structures following the current passive mixer in wireless receivers. Their transfer functions are studied in this section. At DC, the in-band trans-impedance gain is set by the feedback resistance. Figure 2.3: State-of-the-Art Filtering TIA topologies

17 CHAPTER 2. TRANS-IMPEDANCE AMPLIFIEROVERVIEW 5 In Figure 2.4, a large shunt capacitance C s is used between the virtual ground of the Op-amp and ground to filter out the far away interferers when the loop gain of the amplifier decreases. It is a conventional low pass filter consist of a single pole introduced by R 1 C 1, so the attenuation in the filter stop-band is less compared to the filtering TIAs in Figure 2.3 b) - d). R 1 RF Mixer I IN C 1 V OUT Cs Cs C 1 R 1 Figure 2.4: Filtering TIA - Single Pole Virtual Ground with Large Grounded Capacitance The transfer function of this structure is: (2.1) As shown in the equation (2.1), the shunt capacitor C s is not taken into account because the amplifier is ideal and has an infinite gain bandwidth product. In fact, there will be more poles introduced when finite gain bandwidth product (GBP) ω t of the amplifier is considered and it is modeled by an integrator ω t /s. Now the transfer function simplifies to: (2.2) This structure is mainly limited by the number of poles and the GBP of the amplifier in terms of selectivity (stop-band attenuation).

18 CHAPTER 2. TRANS-IMPEDANCE AMPLIFIEROVERVIEW 6 The circuit used in [1] shown in Figure 2.5, the input current is fed to a CR filter followed by an integrator as in Figure 2.4. An additional real pole is created by R 2 C s and they can also be used to control the feedback factor of the amplifier. This type of filter is usually referred as a biquad low pass filter. R 1 C 1 RF Mixer I IN R 2 V OUT Cs Cs R 2 C 1 R 1 Figure 2.5: Filtering TIA Two Real Poles with Switchable Compensation Biquad low pass filter has the following transfer function: (2.3) The transfer function of this structure is: (2.4) { (2.5)

19 CHAPTER 2. TRANS-IMPEDANCE AMPLIFIEROVERVIEW 7 From equation (2.4), it is clear that the filter has two real poles, one at R 1 C 1 and one at R 2 C S. The average filter cut-off frequency can be estimated by equation (2.5). For real pole systems, the quality factor Q in equation (2.5) is always less or equal to 0.5 [5], resulting in a poor selectivity both out-of-band and in-band, depending on the two poles location. However, there will be no peaking in the bode plot or overshoot in time-domain step response which tends to be more stable. In Figure 2.6, a well-known filter topology is shown which is called Tow-Thomas Biquad Filter. R 3 R 1 Mixer I IN C 1 R 2 C 2 RF OP1 OP2 V OUT R 2 C 1 C 2 R 3 R 1 Figure 2.6: Filtering TIA - Tow-Thomas Biquad Filter The transfer function of this structure is: (2.6) { (2.7)

20 CHAPTER 2. TRANS-IMPEDANCE AMPLIFIEROVERVIEW 8 With this topology, the filter cut-off frequency is the same as the previous one, but the two poles can be complex-valued and conjugate pairs, ω p1 = ω p2 * in this case, (i.e. Q > 0.5) and it is governed by the ratio of the RC elements in equation (2.7). This topology is often used due its ease of design. The gain can be controlled by varying a single resistance R 1 and the Q factor can be adjusted by varying a single resistance R 3. The distortion (e.g. third order intermodulation product IM3) is large when the input signals increase. In this kind of feedback structure, the largest signal is defined by the feedback factor that is related to R1 which is usually large, so the overall loop gain of this structure is also large due to the open-loop gain of the op-amps. Since the feedback is connected to the second op-amp, it requires an even higher open-loop gain and bandwidth of the op-amp resulting in high power consumption in order to reduce the nonlinearity. In Figure 2.7, another popular filtering TIA is presented used in [2] called current driven Rauch Biquad filter. R 1 C 1 RF Mixer I IN R 2 V OUT Cs Cs R 2 C 1 R 1 Figure 2.7: Filtering TIA Current Driven Rauch Biquad Filter The transfer function of this structure is: (2.8)

21 CHAPTER 2. TRANS-IMPEDANCE AMPLIFIEROVERVIEW 9 { (2.9) As expected, the transfer function in equation (2.8) is also a biquad with the cut-off frequency set by the two time constants R 1 C s and R 2 C 1. The reason it is used in [2] is because it can be easily tuned(i.e. gain re-configurability) to improve the handling capability of different high-level outof-band interferers (more robust to fading) and while the current going into the virtual ground through R 2 will have a low input impedance to better meet the requirement at the output of the mixer. The noise of this structure can also be reduced by decreasing the grounded capacitance C 1, with a cost of higher input impedance [2]. The linearity of the structure can be improved by increasing the open-loop gain of the op-amp. The higher the open-loop gain is, the smaller the voltage swing at the virtual ground node is which results in a higher linearity with a given output swing. However, these advantages come at a cost of area which means a large capacitor to ground (C s ) is required as in Figure 2.4 and Figure 2.5 to handle the large interferers to minimize the swing at the input of the TIA. 2.3 TIA Input Impedance and Comparison For all the filters introduced in the previous section, every TIA filter topology has its own advantages and disadvantages, this section will focus on the analysis of input impedance of the state-of-the-art TIA filter topology. Figure 2.3 a-b) TIA topologies are first order filter, and the dual real-pole filter respectively, which are quite different from the latter two and from the proposed design. Therefore, comparing with the Tow-Thomas and Rauch Filter structures shown in Figure 2.3 c-d) in terms of input impedance will be the main focus in this section. All of these filters have utilized the advantage of the virtual ground of the Op-Amp. Current going into the virtual ground node will have a small voltage swing due to the size of the input capacitance at high frequencies. This voltage swing at the input node divided by the current is the actual input impedance at that frequency.

22 CHAPTER 2. TRANS-IMPEDANCE AMPLIFIEROVERVIEW 10 First of all, to better compare the input impedance characteristics, it is necessary to study the shape of the profile and effect on its related parameters. Since all the equations for the filter cutoff frequencies and Q factors are obtained in the previous section, it is possible to compare all filter structures assuming they have the same total capacitance (capacitors occupy the most area), cut-off frequency, quality factor, and in-band gain. In this case, a total capacitance of 100pF for a fully differential structure is assumed. The filter cut-off frequency is 3.2MHz (same as in [2]) with a quality factor of and in-band transimpedance gain is 5kΩ single-ended. In Figure 2.6, the Tow-Thomas filter has an input impedance expression of: (2.10) From (2.10), it can be clearly seen that it is a band-pass shaped input impedance. At DC, the input impedance is theoretically zero. For band-pass shaped responses, at the resonant frequency, the maximum value is R 3. Next step is to solve equations using equation (2.7) to get the circuit parameter values for the given specifications: Table 2.1: Design specifications and circuit parameters for Tow-Thomas Filter In-Band Trans-Impedance Gain Cut-off Frequency f -3dB 5 kω 3.2 MHz Quality Factor R 1 R 2 R 3 C 1 C 2 5 kω 1.24 kω 0.88 kω 40 pf 10 pf

23 CHAPTER 2. TRANS-IMPEDANCE AMPLIFIEROVERVIEW 11 Table 2.1 summarized the computed parameters values for the Tow-Thomas Filter to meet the same design specifications as the other filters. Figure 2.8 shows that the input impedance of the Tow-Thomas structure is indeed band-pass shaped with peak value equal to R 3, and it is mainly limited by the size of R 3 and other circuit parameters but increasing GBP ω t of the Op-Amp will not improve the in-band input impedance Gain (dbω) K 1M 10M 100M Frequency (Hz) 1G Figure 2.8: Bode Plot Input Impedance of Tow-Thomas Filter with varying GBP In Figure 2.7, the Rauch Filter s input impedance is somehow equivalent as a RLC resonant circuit [2]. The inductance L is synthesized by the gyrator R 1 and the integrator 1/R 2 C 1. At low frequency, the inductance creates a virtual ground while beyond the cut-off frequency the input impedance is set by the grounded capacitance C s. At the cut-off frequency, the circuit resonates so the inductance and capacitance cancel out. The input impedance reaches its maximum which is equal to R 2. The input impedance expression is: (2.11)

24 Gain (dbω) CHAPTER 2. TRANS-IMPEDANCE AMPLIFIEROVERVIEW 12 Since the ground C s capacitance in fully differential structure is half sized (when placing the capacitor between the differential inputs), the Rauch filter input capacitance can be a few times bigger than the other structures when computing the single-ended values for the same design specifications, but total capacitances still add up to 100pF. Table 2.2: Design specifications and circuit parameters for Rauch Filter In-Band Trans-Impedance Gain Cut-off Frequency f -3dB 5 kω 3.2 MHz Quality Factor R 1 R 2 C 1 C s 5 kω Ω 13.4 pf pf K 1M 10M 100M Frequency (Hz) 1G Figure 2.9: Bode Plot Input Impedance of Rauch Filter with varying GBP

25 CHAPTER 2. TRANS-IMPEDANCE AMPLIFIEROVERVIEW 13 From equation (2.11), the band-pass shaped input impedance reaches its maximum (R 1 R 2 )/(R 1 +R 2 ) which is exactly R 1 in parallel with R 2. If R 1 >> R 2, the impedance is approximately equal to R 2. From Figure 2.9, it shows that the change in GBP ω t of the OP-Amp only has a small effect on the peak value and cut-off frequency of the impedance curve. From the plot and Table 2.2, it can be verified that when R 1 >> R 2, the maximum value is certainly R 2. So the input impedance of the Rauch filter is mainly limited by the circuit parameters as well. Now, it seems that Rauch structure is much better than the Tow-Thomas structure in terms of input impedance when taking the same total capacitance utilizing the advantage in differential structure. 2.4 TIA Noise and Comparison Analog integrated circuits (IC) often have many different performance criteria to that must be met to achieve the required specifications [5]. Noise often limits the value of the smallest useful signals, and linearity often limits the largest useful signals that can occur in the circuit. Therefore, linearity and noise together determines an important term - dynamic range (DR) of a circuit. The Spurious-Free Dynamic Range (SFDR) of a circuit or a system is defined to be the range between the small detectable signal (i.e. when power of the signal is slightly above the noise level), and the largest signal without creating detectable distortions (i.e. when power of distortion power equals to the noise power) in the bandwidth of interest [5]. This section will focus on studying the noise of the state-of-the-art TIAs. The total amount of noise introduced by typical filters is generally proportional to kt/c and inband integrated noise is more critical in filter designs. Once the noise floor level is defined, the amount of total capacitance is roughly set. Therefore, it is better to compare these filters in terms of noise with the same total amount of capacitance as did in the previous section. In theory, these noise sources have their own transfer functions which can be studied in detail to better get a sense what the overall output noise should be. Figure 2.10 shows the Tow Thomas structure along with its noise sources which are mainly from the resistors and op-amp noises, including thermal noise and flicker noise. Noise Transfer functions of the Tow-Thomas Filter at the output due to each noise elements are listed from equation (2.12) to (2.16). Figure 2.11 shows the bode plots for these transfer functions. The noise performance of this structure is poor, since all noise elements exhibit a flat in-band noise shaping

26 CHAPTER 2. TRANS-IMPEDANCE AMPLIFIEROVERVIEW 14 and low-pass shaping out-of-band. Notice that in the bode plot shown in Figure 2.11 b) and e), the zero and pole cancelled each other so the roll-off in the filter stop-band is only -20dB/dec. Most of the in-band gain are higher than 0dB (i.e. Figure 2.11 b) to e)) which means that the noise will be amplified and pass onto the next stage. The overall output noise (sum of the noise transfer functions) will have a flat shaping in-band with a positive DC gain in db excluding the flicker noise at low frequency. Vn R1 2 Vn R3 2 R 3 R 1 Vn op1 2 C 1 Vn R2 2 R 2 C 2 Vn op2 2 From Mixer OP1 OP2 V OUT R 2 C 1 C 2 R 3 R 1 Figure 2.10: Tow-Thomas Filter with Noise Sources (2.12) (2.13) (2.14)

27 Gain (db) CHAPTER 2. TRANS-IMPEDANCE AMPLIFIEROVERVIEW 15 (2.15) (2.16) 0-20 Gain (db) K 1M 10M 100M 1G Frequency (Hz) (a) V OUT / Vn R1 2 Output Noise Transfer Function K 1M 10M 100M 1G Frequency (Hz) (b) V OUT / Vn R2 2 Output Noise Transfer Function

28 Gain (db) CHAPTER 2. TRANS-IMPEDANCE AMPLIFIEROVERVIEW 16 0 Gain (db) K 1M 10M 100M 1G Frequency (Hz) (c) V OUT / Vn R3 2 Output Noise Transfer Function 10 Gain (db) K 1M 10M 100M 1G Frequency (Hz) (d) V OUT / Vn OP1 2 Output Noise Transfer Function K 1M 10M 100M 1G Frequency (Hz) (e) V OUT / Vn OP2 2 Output Noise Transfer Function Figure 2.11: Tow - Thomas Filter Noise Transfer Functions with Each Noise Source

29 CHAPTER 2. TRANS-IMPEDANCE AMPLIFIEROVERVIEW 17 Vn R1 2 R 1 C 1 Vn R2 2 R 2 Vn op 2 From Mixer V OUT Cs Cs R 2 C 1 R 1 Figure 2.12: Rauch Filter with Noise Sources For Rauch filter structure with all the noise elements included as shown in Figure 2.12, equations (2.17) to (2.19) are the noise transfer functions at the output due to each elements, while Figure 2.13 shows the bode plot of each noise element with the same parameter sizes (assuming a total capacitance of 100pF). Noise due to R 1 is flat in-band which is same as the signal transfer function while noise due to R 2 and the op-amp are high-pass shaped in-band due to the zero at R 1 C s. The high-pass noise shaping mechanism in current filters explained in [5] would help to contribute less to the output integrated noise, because it starts with 0dB and go up at 20dB/dec towards cut-off frequency while most Tow-Thomas filter noise transfer functions start with R 1 /R 3 (from equation 2.13 to 2.16) that is higher than 0dB. There is a trade-off between in-band noise and input impedance in both cases. Noise can be reduced by increasing R 3 at the cost of a higher input impedance, while in Rauch filter reducing C s would also push the zero further to lower the amplification of the noise but the input impedance (R 2 ) would increase to maintain the same cut-off frequency and Q factor. (2.17) (2.18)

30 Gain (db) Gain (db) CHAPTER 2. TRANS-IMPEDANCE AMPLIFIEROVERVIEW 18 (2.19) K 100K 1M 10M 100M Frequency (Hz) (a) V OUT / Vn R1 2 Output Noise Transfer Function K 100K 1M 10M 100M Frequency (Hz) (b) V OUT / Vn R2 2 Output Noise Transfer Function

31 CHAPTER 2. TRANS-IMPEDANCE AMPLIFIEROVERVIEW Gain (db) K 100K 1M 10M 100M Frequency (Hz) (c) V OUT / Vn OP 2 Output Noise Transfer Function Figure 2.13: Rauch Filter Noise Transfer Function with Each Noise Source 2.5 Summary Table 2.3: Summary of State-of-the-Art TIA Topologies and Comparison TIA Structure Figure 2.3 a) Figure 2.3 b) Figure 2.3 c) Figure 2.3 d) Single pole Two real pole Tow-Thomas Current Driven Rauch Selectivity(Stopband attenuation ) Low Medium High High Input Impedance High Medium Medium Low Linearity Low Medium Medium High Noise High Medium Medium Low Area Large Medium Large Small Power High Medium Medium Low

32 CHAPTER 2. TRANS-IMPEDANCE AMPLIFIEROVERVIEW 20 This chapter summarizes the state-of-the-art TIAs that are widely used in filter design, especially for RF current mixers. Table 2.3 shows a rough comparison between these designs in terms of filter response, input impedance, noise, linearity, area and power consumption. The two biquad structures that have complex poles called Tow-Thomas and Rauch Filters are studied in detail in terms of signal transfer function, input impedance, and noise. To have a fair comparison, the parameters in the structures are sized to have the same total capacitance, cut-off frequency and Quality factor. Both structures have an advantage that they are easily reconfigured. However, in fully differential structures, Rauch filter has the advantage that the capacitor to ground can be half-sized and connect both terminals to common-mode, which results in a lower input impedance. The noise of the Rauch filter also benefits from the in-band high-pass shaped transfer functions which is also better than the Tow-Thomas filter. The linearity of the Rauch filter can be improved by tuning the single op-amp while Tow-Thomas filter has two op-amps and the second op-amp needs to be more power hungry. In conclusion, Rauch filter is the better state-ofthe-art TIA structure.

33 CHAPTER 3. PROPOSED TRANS-IMPEDANCE AMPLIFIER 21 Chapter 3 Proposed Trans-Impedance Amplifier 3.1 Structure and Transfer Function C F R F I IN + I IN - V OUT - V OUT + C IN C IN C 3 C 3 R F C 1 C 1 C F R 1 R 1 R 2 R 2 C 2 R 2 R 2 Figure 3.1: Original Filtering TIA with active feedback network In Figure 3.1, the filtering TIA in [3] is presented. The basic idea of this reference design is to use the active feedback network that contains three zeros, two at DC and one at R 2 C 2, to connect to the single pole feed-forward loop, so this will allow a sharper transition between in-band and out-of-band regions thus increasing the order of the closed-loop filter response. The design in [3] only aimed to achieve large interferer attenuation out-of-band and high 1-dB compression point where the maximum input current it can handle is 10mA out-of-band. The total current consumption in [3] is 17mA and total capacitance used is in hundreds of pf (area times capacitance density).

34 CHAPTER 3. PROPOSED TRANS-IMPEDANCE AMPLIFIER 22 The proposed design uses the similar idea as in [3]. In order to have two complex poles in the closed loop transfer function to obtain a 2 nd order low-pass profile, two real zeros are needed in the feedback network as shown in Figure 3.1. One zero is at DC implemented by C1, and one is at 1/R 2 C 2 implemented in the feedback network with a class-ab operational trans-conductance amplifier (OTA) to achieve the adaptivity. In the filter pass-band, the filter works as a conventional TIA with the trans-impedance gain set by the feedback resistor R 1 because both capacitor C 1 and C 2 are high impedance at low frequency. On the contrary, in the filter stop-band, the capacitance C 1 is boosted by draining the high-frequency component of the input current interferer (I INT ) before entering into the virtual ground of the feed-forward Op-Amp (I TIA ). Theoretically, the capacitor C 1 can absorb out-of-band interferers without any swing at the input of the TIA, which ensures a low input impedance to improve the linearity of the passive mixer. Furthermore, since one of the terminals of C 1 is connected to the output of the OTA in the feedback network, it can easily swing rail-to-rail without affecting the input swing on the other side of the terminal of C 1. Due to this property, the size of the capacitor C 1 to absorb a given amount of input current can be much smaller compared to the other state-of-the-art filters discussed in chapter 2 where the voltage swing at the input of the TIA followed by a current passive mixer is usually limited to a few hundreds of mv. R 1 Mixer I IN I TIA RF V OUT Cs Cs C 1 C 1 R 1 I INT R 2 C 2 C 2 C 2 R 2 C 2 Figure 3.2: Proposed Filtering TIA with Adaptive Feedback Network

35 CHAPTER 3. PROPOSED TRANS-IMPEDANCE AMPLIFIER 23 The transfer function of the proposed design is as the following: (3.1) { (3.2) The proposed design has a similar form in terms of transfer function in equation (3.1) as the other filters mentioned in Chapter 2. The filter cut-off frequency is defined by the two time constants R 1 C 1 and R 2 C 2. The quality factor Q is a ratio of the two time constants. In order to make the filter a biquad, Q is set to be equal to to achieve the flattest passband frequency response with no peaking or no overshoot in the step-response. The proposed TIA is targeted to achieve the same cut-off frequency and quality factor as the Rauch Filter in [2] which is 3.2MHz to address WCDMA standard which is 1.92MHz channel bandwidth, and respectively to better compare the two designs in terms of area, noise, and input impedance essentially. Transfer functions of TIA current and Interferer current over Input current of the proposed design: (3.3) (3.4)

36 CHAPTER 3. PROPOSED TRANS-IMPEDANCE AMPLIFIER K 1M 10M 100M Frequency (Hz) I INT /I IN (db) I TIA /I IN (db) 100K 1M 10M 100M Frequency (Hz) Figure 3.3: Bode plot - Transfer function of TIA current and Interferer current over Input current The low-pass shape of I TIA /I IN and high-pass shape of I INT /I IN are clearly shown in Figure 3.3 and their transfer functions in equation (3.3) and (3.4) respectively. The two zeros in the feedback network can be clearly seen in equation (3.4). Within the pass-band, the amount of interferer current I INT drained by capacitance C 1 is increasing 20dB/dec towards the filter cut-off frequency ω 0. In the filter stop-band, all the input current should be drained by the capacitance C 1 ideally, since I TIA attenuates at high frequency following the signal transfer function (STF).

37 CHAPTER 3. PROPOSED TRANS-IMPEDANCE AMPLIFIER Finite Trans-Conductance and Gain Bandwidth Product The transfer function is shown in the previous section with ideal components (infinite GBP of the feed-forward Op-Amp, and infinite trans-conductance OTA). However, in fact, the OTA in the feedback network introduces a pair of complex conjugate poles in the feedback network due to finite trans-conductance gm, which become a pair of complex zeros in the closed-loop transfer function. The new transfer function now becomes: (3.5) (3.6) { As shown in the equation (3.5), the finite trans-conductance gm indeed introduced two complex zeros in the closed-loop transfer function, which is located at ω z. It can be seen from equation (3.6) that the cut-off frequency ω 0, ω z and quality factor Q become functions of gm now. It is crucial to analyze the impact due to the finite trans-conductance gm introduced to the system. First, the simplest equation in (3.6) is the zero location ω z which is directly proportional to the trans-conductance gm. Therefore, it sets a constraint when choosing the value for the gm. The zeros have to be placed at least one decade (10 times) after the filter cut-off frequency to keep the in-band response flat, to obtain a larger attenuation after one decade with -40dB/dec roll off and to be independent of the magnitude of the out-of-band interferers. With trans-impedance gain of 5kΩ, it sets a constraint for the gm: 20 ms (3.7)

38 CHAPTER 3. PROPOSED TRANS-IMPEDANCE AMPLIFIER 26 In (3.6), the quality factor now becomes much complicated to see the impact with the finite gm, but the value gets closer to as gm increases shown in the following plot Figure 3.4. Quality Factor Trans-Conductance gm (Siemens) Figure 3.4: Quality Factor as a Function of varying Trans-Conductance gm The impact on the Quality factor of the circuit due to finite trans-conductance gm is plotted in Figure 3.4. This plot is obtained by keeping all the other parameters (i.e. resistors and capacitors) the same, and from the plot, the minimum gm required to keep the quality factor within 3% from the ideal value is 20mS with Q equal to To see the effect on the filter cut-off frequency ω 0, in the denominator, left side should be much bigger than the right side (3.8) By substituting the gm with 20mS into equation (3.8), the left side is indeed more than one hundred times bigger than the right side.

39 CHAPTER 3. PROPOSED TRANS-IMPEDANCE AMPLIFIER Gain (dbω) ω z 40 db K 1M 10M 100M Frequency (Hz) 1G 0 Phase (Degree) ω z ω z K 1M 10M 100M Frequency (Hz) 1G Figure 3.5: Bode plot Transfer Function and Phase Response of the TIA with Increasing Trans-Conductance gm Figure 3.5 is a bode plot that shows the finite trans-conductance gm provided by the OTA that can be used to adjust the location of the complex zeros in the closed-loop transfer function. (i.e. ω z increases as gm increases from 10mS to 50mS). Notice that as the gm increases, it behaves more as a notch filter at that particular narrow frequency range with a high Quality factor thus improving the filter selectivity with more attenuation, but when the response goes back up reducing the attenuation, the power on the OTA can be mainly controlled to provide higher transconductance to get the required out-of-band attenuation according to different design

40 CHAPTER 3. PROPOSED TRANS-IMPEDANCE AMPLIFIER 28 specifications. This adds a degree of freedom in design optimization. As mentioned above, gm has to be at least 20mS to have a minimum impact to keep the filter cut-off frequency and quality factor. In Figure 3.5, gm is verified to be at least 20mS to have the zeros one decade after the filter cut-off frequency and a -40dB attenuation at higher frequencies shown in the plot. Therefore, the minimum requirement for the trans-conductance gm of the OTA is defined. Now, the finite GBP ω t of the Op-Amp in the feedforward path has to be taken into account. The transfer function considering only GBP ω t of the Op-Amp now becomes: (3.9) As discussed above, if the trans-conductance gm is infinite, the complex zeros are at infinity which is not the real case. From transfer function (3.9) excluding finite gm, it can at least help to define the minimum GBP ω t of the Op-Amp to have minimum impact on the closed-loop transfer function, { (3.10) Since the target of the filter cut-off frequency should be able to configure from WCDMA standard to LTE20 standard 10MHz, the Op-Amp GBP ω t has to be sufficient large to satisfy the equation (3.10). Now, considering all finite parameters including trans-conductance gm, GBP ω t and also the second pole ω p2 of the op-amp, the input shunt capacitor to ground C s is now useful to drain the very far-away interferers when the loop gain of the op-amp drops. The overall transfer function becomes more complicated to show and analyze. Figure 3.6 shows the overall transfer function bode plot with increasing in gm as in Figure 3.5. The op-amp finite parameters and C s together created more complex poles resulting in a steeper roll-off at high frequencies which improves the selectivity. A few db peaking effect is due to the notch effect created by the gm as shown in Figure 3.5 and shunt capacitor along with finite GBP of the op-amp together. In later sections, it will discuss the stability of the peaking effect and introduce a way to bias the OTA to lower the peaking effect and an adaptive transfer function will be realized.

41 Phase (Degree) CHAPTER 3. PROPOSED TRANS-IMPEDANCE AMPLIFIER 29 Gain (dbω) K 1M 10M 100M Frequency (Hz) K 1M 10M 100M Frequency (Hz) Figure 3.6: Bode plot Transfer Function and Phase Response of TIA With Real Parameters

42 CHAPTER 3. PROPOSED TRANS-IMPEDANCE AMPLIFIER Reconfigurable TIA Filter R 1 Mixer I IN RF V OUT Cs Cs C 1 C 1 R 1 I INT R 2 C 2 αc 2 αc 2 R 2 C 2 Figure 3.7: Proposed Filtering TIA with Reconfigurable Cut-off Frequency Another target of the TIA is to be reconfigurable between WCDMA standard and LTE standard up to 20MHz optimistically. Unit sized capacitors are used to build up the capacitor banks for reconfigurability. Simple MOS switches will be used to control all these binary weighted capacitors. Therefore, minimizing the number of tuning parameters should be the primary goal to save more pins on the pad and area consumed by the MOS switches. The circuit now introduces a constant α which is a multiplier of the first C 2 in the feedback network as shown in Figure 3.7. The circuit transfer function and its associated parameters become the following: (3.12)

43 CHAPTER 3. PROPOSED TRANS-IMPEDANCE AMPLIFIER 31 (3.13) { From equation (3.12) and (3.13), it is clear that the constant α does not affect any of the equations but a simple multiplying constant. In this way, it saves more pins and area instead of tuning every parameters of the filter which will limit the circuit performance since the MOS switches will introduce parasitic capacitances and small-signal resistance in triode region. In the receiver chain, the low-noise amplifier (LNA) and mixer together provide a trans-conductance of about 40mS, thus the overall gain of the receiver chain sets the TIA gain to have a very low tuning range regarding to the specifications. The location of the zeros will be always at least one decade after the poles as seen in equation (3.7) if R 1 is fixed and gm > 20mS. So the circuit tuning is done by varying R 2, C 1 and α. In order to keep the same quality factor in (3.13), since R 2 is in the numerator, αc1 in the denominator must decrease the same multiplier as R 2. By rearrange these equations, it is possible to get the equations among these circuit parameters, such as the following: { (3.14)

44 Phase (Degree) CHAPTER 3. PROPOSED TRANS-IMPEDANCE AMPLIFIER 32 Gain (dbω) K f -3dB = 16.9MHz f -3dB = 3.11MHz 1M 10M 100M Frequency (Hz) K f -3dB = 15.8MHz f -3dB = 3.15MHz 1M 10M 100M Frequency (Hz) Figure 3.8: Bode Plot Transfer Function of Amplitude and Phase Response with Reconfigurable Cut-off Frequency Figure 3.8 shows the reconfigurable TIA bode plot tuned from 3.11MHz to 16.9MHz taking all the non-ideal parameters into account with gm = 20mS, ω t much greater than in (3.10), and varying C s by scaling R 2, α, and C 1 while keep other parameters and the quality factor the same.

45 CHAPTER 3. PROPOSED TRANS-IMPEDANCE AMPLIFIER 33 Among the tuning ranges, the entire plots exhibit the same biquad behaviour with -40dB/dec roll off after the cut-off frequency and the quality factor for all these cases are Q The reason why the highest bandwidth cannot achieve 19.1MHz with the theoretical equation (3.2) is because the fixed finite gm and GBP ω t at 200MHz affects the transfer function more significantly than the lowest bandwidth case, but the gain peaking effect with higher bandwidth is less since the complex zeros are already at high frequency and C s takes into account regarding to ω t. Moreover, it can be verified in the plot that complex zeros are always one decade after the cut-off frequency due to the finite gm which is 20mS. This enhances the advantage that controlling the zeros not only improves the selectivity but will not affect the in-band response or the cut-off frequency. Finally, the shunt capacitor C s could be a few times smaller than the Rauch filter and it will not affect the in-band response thus providing another degree of freedom to tune the filter according to different bandwidths and specifications. Table 2.1 below summarizes the design specifications and circuit parameters used in Figure 3.8. Table 2.1: Design Specifications and Circuit Parameters for the Reconfigurable TIA Cut-off Frequency f -3dB (MHz) (in Figure 3.8) Quality Factor Op-Amp GBP ω t (MHz) OTA gm (ms) In-Band Gain R1(kΩ) R 2 (kω) C 1 (pf) C 2 (pf) αc 2 (pf) C s Single-Ended (pf) Total Capacitance - Fully Differential (pf)

46 CHAPTER 3. PROPOSED TRANS-IMPEDANCE AMPLIFIER Input Impedance (3.15) 40 Gain (dbω) 30 ω t gm C s 0 100K 1M 10M 100M Frequency (Hz) 1G Figure 3.9: Bode Plot Input Impedance Transfer Function of Proposed TIA Filter with Varying Parameters Since the input of the proposed TIA is directly connected to the virtual ground of the Op-Amp, at low frequency, the impedance should be zero in theory. Equation (3.15) shows the input impedance of the TIA is not zero when finite GBP ω t is considered. It is also a band-pass shaped and at the cut-off frequency, the maximum value should reach 1/(αC 1 ω t ) by simplifying equation. The input impedance plot for the WCDMA base case with cut-off frequency at 3.2MHz is shown in Figure 3.9. The full transfer function equation is too complicated to show, so the graph has intuitively shown the effect on the input impedance curve due to each parameter in the filter including ω t, C s and gm. The first zero is at DC, and the peak value of the band-pass shaped curve has more effect when increasing the GBP ω t. The finite trans-conductance gm has introduced a pair of zeros which causes a 20dB/dec rising after the peak which is due to the first two poles. In order to make the input impedance low-pass shaped, the shunt ground capacitance

47 CHAPTER 3. PROPOSED TRANS-IMPEDANCE AMPLIFIER 35 C s has to play an important role to lower the input impedance at high frequency which introduces two poles around the zeros location. The final input impedance transfer function including these non-ideal parameters should have 4 poles and 3 zeros. Notice that the C s capacitance is only 48pF, other capacitance C 1,C 2 only contribute 52pF while in the Rauch Filter C s is 146pF which is 3 times bigger, and the maximum impedance level is higher as well. Therefore, using same amount of total capacitance in these structures, the proposed TIA has the lowest input impedance. In other words, for the other filters (Tow-Thomas and Rauch) to get the same level of input impedance as the proposed TIA, the capacitances needed (the area) would be much bigger. The ω t requirement which is directly related to power consumption of the Op-Amp in other designs may not be as strict as the proposed design. Since the maximum input impedance level is related to 1/(αC 1 ω t ), it has an interesting characteristic when reconfiguring the filter frequency. Bring back the equations in (3.13) for the filter cut-off frequency and quality factor, it can be noticed that scaling R 2, α, and C 1 as in the previous subsection would have the lowest number of tuning parameters while keeping the inband gain R 1 and the quality factor the same for all bandwidths. However, considering the max input impedance, 1/(αC 1 ω t ) will now be increasing since αc 1 is scaled down for higher bandwidth. In the following Figure 3.10 a), it shows that the max input impedance level increases as the bandwidth of the filter increases by scaling down R 2, α, and C 1. Another option to re-configure the filter to keep the same quality factor and low input impedance is by scaling down R 1, R 2 and both C 2 to keep the lowest input impedance possible as shown in Figure 3.10 b). This option can be used if there is a strict specification on the input impedance and a low in-band gain is needed. This is the trade-off between input impedance and in-band gain when tuning the circuit. The trade-off for low input impedance in other state of the art filters discussed in Chapter 2 mainly comes at the cost of area (input capacitance and size of the resistor), while the trade-off in the proposed design mainly comes from the finite gain bandwidth of the op-amp which is the power.

48 CHAPTER 3. PROPOSED TRANS-IMPEDANCE AMPLIFIER 36 Gain (dbω) 50 f -3dB = 16.9MHz Case 40 Gain (dbω) f -3dB = 3.11MHz Case K 1M 10M 100M Frequency (Hz) (a) 1G 30 f -3dB = 16.9MHz Case f -3dB = 3.11MHz Case 0 100K 1M 10M 100M Frequency (Hz) (b) 1G Figure 3.10: Bode Plot Input Impedance of Proposed TIA Filter with Reconfiguring Bandwidth and Scaling Options

49 CHAPTER 3. PROPOSED TRANS-IMPEDANCE AMPLIFIER Spurious-Free Dynamic Range Noise Transfer Functions and Analysis Vn R1 2 R 1 Vn op 2 From Mixer OP V OUT C 1 C 1 R 1 Vn R2 2 R 2 C 2 Vn gm 2 C 2 C 2 R 2 C 2 Figure 3.11: Proposed TIA Filter with Noise Sources (3.16) ( ) (3.17)

50 CHAPTER 3. PROPOSED TRANS-IMPEDANCE AMPLIFIER 38 ( ) (3.18) ( ) (3.19) Equation (3.16) is the noise transfer function from R 1 to the output. It is clear that it behaves the same as the filter transfer functions which is a flat band shaping in-band since the transimpedance resistor R 1 will simply amplifies the noise along with it. For equation (3.17) to (3.19), it is obvious that there are zeros in the numerator which means it is a high-pass shaped in-band response. It can be understood intuitively from Figure 3.11 with the noise sources appeared in the circuit diagram. At low frequencies, the capacitor C 1 and C 2 are high impedance, there is no noise injected into the feedback network, and the noise generated by the noise sources in the feedback network cannot be injected into the feed-forward path, thus reducing the total output noise at low frequency. In the bode plot Figure 3.12 b) and d), these can be verified that the first zero is at DC, therefore the transfer function plot starts below 0dB and rise up at 20dB/dec towards the cut-off frequency. The plot is generated by reconfiguring the TIA as done in subsection When reconfiguring the TIA, αc 1 and R 2 is scaled down mostly while R 1 stays constant, thus making the complex poles moving further. The first zero at C 1 R 1 will keep rising until the cut-off frequency. This unique property offers more benefits to the noise performance compared to the other two designs, because the high-pass shaped noise sources contribute a lot less (below 0dB) than the Rauch Filter (starts with 0dB). Therefore, excluding the flicker noise, the overall output noise transfer function of the TIA will be mostly flat in-band for the lowest bandwidth configuration, while the noise shaping will be slightly going up above 0dB for the highest bandwidth configuration as shown in Figure All the high frequency peaking due the finite GBP ω t and transconductance gm is negligible since in-band noise shaping is the most important in terms of noise performance.

51 Gain (db) CHAPTER 3. PROPOSED TRANS-IMPEDANCE AMPLIFIER Gain (db) K 1M 10M 100M Frequency (Hz) (a) V OUT / Vn R1 2 Output Noise Transfer Function K 1M 10M 100M Frequency (Hz) (b) V OUT / Vn R2 2 Output Noise Transfer Function

52 CHAPTER 3. PROPOSED TRANS-IMPEDANCE AMPLIFIER 40 Gain (db) 10 Gain (db) K 1M 10M 100M Frequency (Hz) (c) V OUT / Vn OP 2 Output Noise Transfer Function K 1M 10M 100M Frequency (Hz) (d) V OUT / Vn gm 2 Output Noise Transfer Function Figure 3.12: Proposed TIA Filter Output Noise Transfer Function with All Noise Source

53 CHAPTER 3. PROPOSED TRANS-IMPEDANCE AMPLIFIER Linearity and Intermodulation Phenomena Due to the same reason and the unique property of the proposed TIA filter, the intermodulation product (IM) generated in the filter passband should also follow the high-pass shaping as the noise transfer function shown in Figure Since the out-of-band interferers are drained by the capacitance C 1 instead of going into the feed-forward path, the IM product generated in the filter passband due to these interferers is also high-pass filtered by C 1, thus providing a high linearity within the filter pass-band. The filter linearity will be mostly limited by the op-amp if there is already IM products in the pass-band at the input, but it will not be limited by the feedback network and the OTA. R 2 C 2 TIA Virtual Ground I INT C 1 C 2 TIA Output C 1 C 2 Magnitude Pass-band Interferers R 2 C 2 Magnitude Pass-band Interferers ω IM3 ω 1 ω 2ω 1 - ω IM3 3ω 1-2ω IM3 ω IM3 ω 1 ω 2ω 1 - ω IM3 3ω 1-2ω IM3 Figure 3.13: Proposed TIA Filter Intermodulation Product Phenomena

54 CHAPTER 3. PROPOSED TRANS-IMPEDANCE AMPLIFIER Stability Analysis Loop 1 R 1 From Mixer V r1 V t1 V r3 V t3 V OUT C 1 C 1 R 1 Main Loop R 2 C 2 C 2 V t2 V r2 C 2 R 2 C 2 Loop 2 Figure 3.14: TIA Loop Gain Analysis All Breaking Points The proposed TIA filter has a few feedback networks as shown in Figure In the main loop, the feedback network consists of the OTA and the zeros created by C1 and R 2 C 2. In the inner loop 1, around the Op-Amp, the feedback is mainly the trans-impedance resistor R 1. In the inner loop2, around the OTA, the feedback network mainly consists of R 2 C 2 in series. While doing loop gain analysis, a test source should be inserted in the breaking points shown in Figure 3.14, so the loop gain will be equal to -Vr x /Vt x [5]. In Figure 3.15, the theoretical bode plot shows the loop gain for the main loop. At low frequencies, the zero due to capacitor C 1 provides the high pass shaped 20dB/dec rising with a phase of -90 degree. Another zero due to R2-C2 provided by the inverting structure around the OTA is introduced causing an increase in phase change while the op-amp finite bandwidth ω t, the second pole ω p created complex poles causing the phase to drop dramatically while the gain drops with almost -60dB/dec up to 1GHz. The phase margins at the two zero crossing point are maintained more than 90 degrees since the OTA s finite bandwidth is not modelled in the theoretical bode plot. A few db gain peaking in the closed-loop transfer function in Figure 3.6 is mainly due to this phase margin but can be compensated by the

55 Phase (Degree) CHAPTER 3. PROPOSED TRANS-IMPEDANCE AMPLIFIER 43 grounded input capacitance C s. As C s increases shown in Figure 3.15, it moves the dominant pole to lower frequency which is created by the op-amp finite gain bandwidth ω t,, and improves the phase margin of the open loop gain. Therefore, the gain peaking does not compromise the stability, but it can be easily controlled by adding more input capacitance. The detailed stability analysis will be studied in Chapter 4 with transistor level implementations Gain (db) C s K 1M 10M Frequency (Hz) 100M 1G K 1M 10M Frequency (Hz) 100M 1G Figure 3.15: TIA Loop Gain Analysis Overall Loop Gain Bode Plot

56 Gain (dbω) CHAPTER 3. PROPOSED TRANS-IMPEDANCE AMPLIFIER Adaptive Filtering Response Due to the filtering effect provided by the input capacitance C 1, it is possible to implement the OTA in the feedback network biased with a small dc current to work in class-ab output stage while still maintaining a high linearity, low noise but uses much less power than class-a circuit. In this way, in the absence of large out-of-band interferers, the OTA still works in class-a with sufficient gm to maintain a good selectivity. In the presence of large out-of-band interferer current I INT drained by C 1, the OTA starts to work in class-ab thus providing higher transconductance gm proportional to the magnitude of the interferer current. The output of the OTA will have a large swing, even rail-to-rail, while the input swing will still be within a few hundred mvs when the TIA is not compressing. Figure 3.16 below shows the bode plot with increasing gm as in Figure 3.6. The dashed lines are the trend of the adaptive transfer function as the magnitude of the interferer current increases. This unique characteristic allows changing the filter selectivity automatically without the need of any control loop, therefore adding another degree of freedom in the design optimization K 1M 10M 100M Frequency (Hz) Figure 3.16: Bode Plot Adaptive Transfer Function Sketch of Proposed TIA with Increasing Interferer Power (Theoretical)

57 CHAPTER 3. PROPOSED TRANS-IMPEDANCE AMPLIFIER Summary This chapter introduced the original TIA topology idea from the reference design and described the major modifications in this design. It studied the proposed design in terms of ideal transfer function, effect of the finite trans-conductance gm, input impedance, noise transfer functions and linearity. Finally the stability of the loop gain is analyzed, and an adaptive filtering profile can be achieved by using a class-ab OTA in the feedback network to achieve the adaptivity.

58 CHAPTER 4. SYSTEM AND CIRCUIT DESIGN 46 Chapter 4 System and Circuit Design This chapter outlines the circuit implementation in transistor level of the proposed TIA. It introduces the implementation of the main op-amp and summarizes the advantages and disadvantages biasing the CMOS inverter OTA in class-a and class-ab; also binary capacitor banks with MOS switches. The stability of each feedback loop is simulated, including the common mode feedback loop. The final simulation results are presented at the end of this chapter. 4.1 Operational Amplifier in Feed-Forward Path From the previous chapter, the most important specification of the op-amp is defined which is the GBP ω t to satisfy (3.10) for all tuning bandwidths. The proposed design uses the common Two-Stage Miller Compensated topology for the main op-amp in the feed-forward path. The two-stage op-amp can provide a high gain and high output swing which is suitable for the proposed TIA. There are some other important specifications of the op-amp need to be determined, such as the dc gain A 0, slew rate, and input thermal noise due to the gm. R 1 I IN V IN -A 0 V OUT Figure 4.1: Conventional TIA First of all, the dc gain A 0 affects the input impedance mostly at low frequency. From Figure 4.1, a conventional TIA, it is clearly seen that V OUT = -A 0 V IN, and is also equal to I IN R 1. By simplifying the equations, V IN /I IN = - R 1 /A 0 and it gives the requirement for A 0 which is greater than 34dB if the input impedance requirement is less than 100Ω. However, 34dB is low compare

59 CHAPTER 4. SYSTEM AND CIRCUIT DESIGN 47 to moderate two-stage op-amp dc gain; therefore the target should be greater than 40dB. Secondly, the slew rate limitation of the TIA is not strictly requirement because the input is a current and going into the virtual ground node. The voltage swing at the input is limited due to a large finite GBP, therefore the output voltage change will not be limited due to slew rate, but the target should be moderate such as 100V/μs. Finally, the thermal noise due to the input pair should be less than a 1kΩ resistor, as in equation (4.1), gm of the input pair is defined to be at least greater than 1mS. Ω (4.1) V 1 R C C C gm 1 V in R 1 C 1 gm 5 V 1 R 2 C 2 V OUT Figure 4.2: Small Signal Model of the Two-Stage Miller Compensated Op-Amp (4.2) (4.3) (4.4) (4.5) (4.5)

60 CHAPTER 4. SYSTEM AND CIRCUIT DESIGN 48 VDD VDD VDD VDD M7 R 1 R 1 V CMFB M9 V CMFB M8 M10 V OUTP V INP M1 M2 V INN VOUTN IBIAS R 1 R 1 RC CC CC RC M5 M3 M4 M6 V OUTP R 1 R 1 VREF V OUTN OP1 V CMFB Transistor Sizing in µm W/L M1,M2 120/0.2 M3,M4 20/1 M5,M6 40/1 M7,M8 20/0.2 M9,M10 10/0.2 Figure 4.3: Two-Stage Miller Compensated Op-Amp for the Proposed TIA Equations (4.2) to (4.6) and Figure 4.2 in the text book [5] provide the main guidance when designing the two-stage op-amp. Figure 4.3 is the full schematic for the op-amp with transistor sizes labelled. The Miller Compensation Capacitor used is 1.3pF, and R C is 1.4kΩ. The first stage input pair gm is about 1.9mS which ensures the GBP ω t satisfies (3.10) with equation (4.3). The bias current used in M 9 and M 10 is 200µA which makes the slew rate of the op-amp with (4.5) is greater than 100 V/μs. The noise of the input pair is less than a 1kΩ resistor since the input gm is almost twice than the calculated value. The input pair W/L ratio is made large enough to have the transistors work in subthreshold region to achieve the highest gm efficiency for a given amount of current. Notice that the second stage transistors do not have to be big and consume a few times more current than the first stage, because the capacitive load αc 2 it drives decreases as the filter bandwidth is tuned larger. Therefore, the second pole location (4.4) is moved far away to make the Op-Amp more stable and gain more phase margin. The size of M 5 is twice as M 3 thus the second stage consumes 200µA current, with roughly twice the gm.

61 CHAPTER 4. SYSTEM AND CIRCUIT DESIGN 49 Length of M 3 and M 4 are also sized large enough to lower the flicker noise contributed to the output while increasing the length improves the gain as well. R 1 in Figure 4.3 are all 100kΩ for the common mode signal and it is sized 20 times larger than the feedback trans-impedance gain resistance in the TIA to minimize the impact to the equivalent resistance seen at the output node. Notice that the common mode feedback signal is connected to the PMOS in the second stage instead of the first stage due to stability issues, since the common mode gain is too large when it feedbacks to the first stage and it is harder to compensate. Therefore, putting the common mode feedback node in the second stage is a better option while still achieving a good accuracy of sensing the common-mode signal (a few mv difference). The current consumption for this common mode feedback circuit is 15µA. VDD VDD M 3 M 4 Transistor Sizing in µm W/L M1,M2 11.2/0.12 M3,M4 0.72/0.12 M5,M6 2/0.5 V OUT VDD V INP M 1 M 2 V INN IBIAS M 5 M 6 Figure 4.4: Common Mode Feedback Amplifier for Two-Stage OP-AMP The total simulated current consumption for the op-amp is approximately 615µA. The open-loop dc gain is 47dB with a phase margin of 50 degree and a GBP of 104MHz for the lowest bandwidth case. Since the loading capacitance is the largest with a cut-off frequency of 3.2MHz, 100MHz GBP is large enough to meet the requirement (3.10) in Chapter 3 without affecting the in-band transfer function. At the other extreme, the GBP is 210MHz for the highest bandwidth case with the smallest loading capacitances.

62 CHAPTER 4. SYSTEM AND CIRCUIT DESIGN Operational Trans-conductance Amplifier in Feedback Network VDD VDD V INP V OUT V INN Figure 4.5: Simplified Scheme for CMOS Trans-conductor The OTA in the feedback network can be implemented using a simple CMOS transconductor as in Figure 4.5 This simple trans-conductor is biased to work in class-a stage only. However, the dc bias current for this class-a transconductor is large to provide a given amount of transconductance gm since it is proportional to μc ox W/L (V GS V T ) and V G is biased at the common mode of the circuit which is half V DD. Class-A amplifiers always conduct during one complete cycle of the input signal waveform thus providing minimum distortions and maximum output swing. Due to the intrinsic high-pass shaping of the noise and distortion produced by the feedback network, the distortions generated at low frequencies are filtered out; the OTA can be biased in class-ab stage without compromising the overall linearity of the TIA and consume less power in the absence of large out-of-band interferers. The only trade-off is between power and area since biasing in class-ab stage would result in a small V eff with a very large W/L ratio and duplicated capacitance C 2, αc 2 and R 2 to provide the same amount of trans-conductance gm (at least 20mS found in Chapter 3).

63 CHAPTER 4. SYSTEM AND CIRCUIT DESIGN 51 R1 R1 VDD VDD OP2 VDD IBIAS V REF VBIAS OP3 VINPPMOS M 3 M 4 V REF VINNPMOS M 5 R1 R1 V OUTN V OUTP VINP NMOS M 1 M 2 VINN NMOS Transistor Sizing in µm W/L M1,M2 240/0.12 M3,M4 240/0.12 M5 240/0.12 V BIAS R1 R1 Figure 4.6: Proposed Operational Trans-conductance Amplifier with Bias in Class-A or Class-AB Figure 4.6 shows the full scheme of the OTA in the feedback network with the biasing circuit. It can be seen that the input voltages are at different common mode level, one is at the NMOS input current source V BIAS, and the other one is at the output of the common mode feedback amplifier OP2 to maintain the OTA output at the common mode level V REF. Consequently, one drawback of this biasing scheme is an extra input node is required so duplicated C 2 R 2, and αc 2 have to connect to the PMOS and NMOS separately. However, the V Eff voltages of the PMOS and NMOS are reduced by about 200mV so the bias current can be reduced which is controlled by the NMOS current mirror. The current mirror NMOS drain voltage is also biased at the common mode level with amplifier OP3 to accurately control the mirrored current. The W/L ratio of the P,NMOS are made sufficiently big to sustain the large current coming from the output node connected to the capacitor C 1 in the TIA. This class-ab operation is clearly shown with the transient simulation results in Figure 4.7.

64 Drain Current (ma) CHAPTER 4. SYSTEM AND CIRCUIT DESIGN 52 Output Voltage(V) µa 2 ma Time (ns) a) µa 2 ma Time (ns) b) Figure 4.7: OTA Output Voltages and Drain Currents with Different Input Current at 50MHz

65 CHAPTER 4. SYSTEM AND CIRCUIT DESIGN 53 Figure 4.7a) and b) shows the output voltages and drain currents respectively, at the node V OUTN and V OUTP with different input current amplitude simulated at 50MHz labelled with blue and black traces. From previous chapter, it is known that the zeros are placed one decade after the filter cut-off frequency which is 3.2MHz. Therefore, at 50MHz the signal should follow the filter transfer function with the zeros introduced as in Figure 3.5. The dc bias current is about 400μA in each branch to provide a total trans-conductance of 20mS to meet the requirement. The black line in Figure 4.7 a) and b) is when input current is small (200uA) so the OTA is still working in class A. The current drained by the OTA is still a perfect sinusoid centered at 400μA, and the output voltage swing is small. The blue line is when input current is large (i.e. 2mA) which is drained by the TIA input capacitor C 1 connected to the output of the OTA, thus forcing the OTA to work in class-ab. The drain current starts to introduce distortions and a half wave plus a portion of the other half is presented in Figure 4.7 b). The voltage at the OTA output is almost rail-to-rail while the input voltage swing is still within a few hundred mv due to the filtering effect provided by C 1. The trans-conductance provided by the OTA is larger when it works in class-ab with large interferer current since it is proportional to the drain current. In the closed-loop transfer function, the attenuation at that frequency is larger due to the bigger trans-conductance gm. Therefore, the filter transfer function established a unique adaptive characteristic depending on the input current beyond frequencies of the zeros location. The input shunt capacitor C s also helps to drain the interferer current at very high frequencies. VDD VDD M 3 M 4 Transistor Sizing in µm W/L M1,M2 8/0.4 M3,M4 2/0.4 M5,M6 2/0.4 VDD VDD M5 M 6 V INP M 1 M 2 V OUT V INN VDD IBIAS V INP M1 M2 V OUT V INN IBIAS M 5 M 6 M3 M4 Transistor Sizing in µm W/L M1,M2 12/0.12 M3,M4 0.8/0.12 M5,M6 2/0.5 Figure 4.8: Common Mode Feedback Amplifiers for OTA

66 CHAPTER 4. SYSTEM AND CIRCUIT DESIGN 54 Figure 4.8 shows the common mode feedback amplifiers used in OTA and their bias currents are both 5μA. The total current consumption of the OTA is approximately 810μA and it is easily adjustable with different selectivity requirements. 4.3 Reconfigurable TIA with MOS switches and Capacitor banks The re-configurability of the TIA is achieved by using a single NMOS switch and binary weighted capacitor banks with a unit capacitance of 0.5pF shown in Figure 4.9. The NMOS switch for C 1 is placed at the input terminal side because the NMOS can only pass signal up to V DD - V TH while input voltage swing is limited to a few hundred mv. It cannot be placed on the other side of C 1 because there might be rail-to-rail swing condition. All other switches are all placed in the proper location with small voltage swings centered at the common mode level. The W/L ratio of the switch is also checked to be large enough to minimize the R DS introduced. V CTRL [0:0] [1:0] [3:0] [7:0] Figure 4.9: Reconfigurable TIA with Switch and Capacitor Banks Figure 4.10 is the top level schematic of the proposed TIA. Although capacitances C 2 and αc 2 needed to be doubled to be biased in such a way to work in class-a or class-ab, the total extra capacitance used is only 24pF which is still small compare to the other state-of-the-art filters.

67 CHAPTER 4. SYSTEM AND CIRCUIT DESIGN 55 R 1 Mixer IIN RF Cs V OUT C 1 C 1 R 1 R 2 C 2 αc 2 αc 2 R 2 C 2 Figure 4.10: Reconfigurable TIA Top Level Schematic 4.4 Stability Analysis The loop gain for the main loop of the filter is simulated and phase margins are shown in Figure 4.11 which is similar as the theoretical plot in Chapter 3. The OTA has a finite bandwidth so the poles in OTA are inverse proportional to the loading capacitance C 1 since total gm used is fixed at around 20mS. For the lowest bandwidth WCDMA case, the zero provided by R2-C2 in the loop gain is supposed to help gain phase, but the poles in the OTA are also at lower frequency which cancels the phase improvement due to the zero. However for the highest bandwidth LTE case, the zero R2-C2 is tuned to higher frequency and the loading capacitance C 1 is smaller thus pushing the poles in OTA at higher frequencies too. The main op-amp bandwidth ω t is not changed by that much after tuning and is also the dominant pole in the main loop gain so the phase margin for the highest bandwidth case is automatically improved. The phase margin at the gain peaking location in the signal transfer function, still has 52 degree of phase margin for lowest bandwidth case, while for the highest bandwidth case phase margin is 107 degrees so the peaking effect is reduced shown in Figure The grounded input capacitance can be used to compensate the stability by moving the dominant pole and improve the phase margin but the

68 CHAPTER 4. SYSTEM AND CIRCUIT DESIGN 56 total capacitance used in this design is around 100pF, so the amount of input grounded capacitance used is limited. Therefore, the gain peaking does not compromise the stability but only reduces the attenuation by a few db with small out-of-band interferers in the worst case. The gain peaking effect is further reduced when there are large interferer currents drained by the class-ab OTA which results in an adaptive filtering profile shown in Figure The other loops are simulated and phase margins of the lowest and the highest bandwidth of typical process are reported in Table 4.1. Phase margin of all PVT corner simulations are verified above 30 degrees. Phase (Degree) Gain (db) PM PM 100K 1M 10M 100M 1G Frequency (Hz) Figure 4.11: Bode Plot Loop Gain of the TIA Main Loop

69 Phase (Degree) Gain (db) CHAPTER 4. SYSTEM AND CIRCUIT DESIGN Gain (db) WCDMA LTE Phase (Degree) LTE 50 WCDMA PM 0 100K 1M 10M 100M Frequency (Hz) PM Figure 4.12: Bode Plot Loop Gain of the Feed-forward Op-Amp WCDMA WCDMA LTE LTE LTE WCDMA WCDMA LTE PM PM 0 100K 1M 10M 100M Frequency (Hz) PM PM 1G Figure 4.13: Bode Plot Loop Gain of the Op-Amp Common Mode Feedback

70 CHAPTER 4. SYSTEM AND CIRCUIT DESIGN 58 Gain (db) WCDMA LTE LTE Phase (Degree) WCDMA LTE PM 0 100K 1M 10M 100M Frequency (Hz) 1G Figure 4.14: Bode Plot Loop Gain of the OTA Common Mode Feedback Table 4.1: Summarized Stability Simulation Results Lowest Bandwidth Highest Bandwidth Main Loop (Degree) Main Op-Amp (Degree) Op-Amp Common-Mode Feedback (Degree) OTA Common-Mode Feedback (Degree)

71 CHAPTER 4. SYSTEM AND CIRCUIT DESIGN Simulation Results 80 Gain (dbω) K 1M 10M 100M Frequency (Hz) Figure 4.15: Bode Plot - Simulated Reconfigurable TIA Signal Transfer Functions Gain (dbω) K 1M 10M 100M Frequency (Hz) Small-Signal 240 μa 400 μa 1.3 ma 2.4 ma 4.0 ma 7.1 ma 1G Figure 4.16: Bode Plot - Simulated TIA Adaptive Transfer Function with Different Input Signal (cut-off frequency at 3.1MHz)

72 Output Output Noise Noise (dbv/ Hz) (dbv 2 /Hz) CHAPTER 4. SYSTEM AND CIRCUIT DESIGN Gain (dbω) K 1M 10M 100M Frequency (Hz) Figure 4.17: Bode Plot- Simulated Reconfigurable TIA Input Impedance Transfer Functions Tow-Thomas Rauch This Work K 100K 1M 10M Frequency (Hz) Figure 4.18: Simulated Output Noise Comparison with State-of-the-Art Designs ( f

73 P OUT (dbm) CHAPTER 4. SYSTEM AND CIRCUIT DESIGN Output Noise (dbv 2 /Hz) K 100K 1M 10M Frequency (Hz) Figure 4.19: Simulated Output Noise Reconfigurable TIA with High-pass Noise Shaping db/db Δ db/db P IN (dbm) Figure 4.20: Two Tone Out-of-Band Linearity and 19.5MHz for Lowest Band Configuration

74 CHAPTER 4. SYSTEM AND CIRCUIT DESIGN 62 P OUT (dbm) db/db Δ 3 db/db P IN (dbm) Figure 4.21: Two Tone Out-of-Band Linearity and 95MHz for Highest Band Configuration (4.6) The third-order input intercept point IIP 3 is calculated without ΔA/2 when the two tones are placed in-band, where the intermodulation products and the two tones exhibit the same gain. However, the IIP 3 measured in this section is done by placing two out-of-band tones at the locations specified in Figure 4.15 and Figure Since the output power at the tone location is attenuated by the filter, ΔA/2 has to be taken into account when calculating the IIP 3 of the filter. The first-order output power shown in Figure 4.15 and Figure 4.16 are at 19.5MHz and 95MHz respectively, where it has an attenuation of 32.5dB and 34.5dB respectively shown in Figure Therefore, with the information in Figure 4.15 and Figure 4.16, the simulated IIP 3 of the filter is calculated to be 47.25dBm and 34.25dBm respectively. The Figure of Merit (FOM) defined as in equation (4.7) is used to evaluate filter performance: (4.6) (4.7)

75 CHAPTER 4. SYSTEM AND CIRCUIT DESIGN 63 where P c is the power consumption of the filter, f -3dB is the cut-off frequency and N is the number of poles, SFDR is the normalized spurious free dynamic range with equation (4.8): ( ) (4.8) where P N is the input referred noise power, integrated over the channel (i.e. WCDMA with 1.92MHz, LTE20 with 10MHz). Other simulation results including cut-off frequencies for reconfigurable bandwidths, the adaptive transfer function for the lowest bandwidth configuration, maximum input impedance, IIP 3 and integrated input referred noise for WCDMA and LTE20 are reported in Table 4.2. Table 4.2: Summary of Simulation Results Circuit Parameters In-Band Gain R1(kΩ) R 2 (kω) C 1 (pf) C 2 (pf) αc 2 (pf) C s Fully Differential (pf) Total Capacitance - Fully Differential (pf) Trans-conductance gm (ms) Simulated Results Cut-off Frequency f -3dB (MHz) (Figure 4.15) DC Power (mw) Number of Poles

76 CHAPTER 4. SYSTEM AND CIRCUIT DESIGN 64 Maximum Differential Input Impedance (dbω) (Figure 4.17) IIP 3 out-of-band (dbm) (Figure 4.20, Figure 4.21) Input Referred Noise Integrated over 1.92MHz, and 10MHz (µv RMS ) (Figure 4.19) n/a n/a n/a n/a n/a n/a n/a n/a 31.8 SFDR out-of-band (db) 87.2 n/a n/a n/a n/a 74.1 FOM db(j -1 ) 183 n/a n/a n/a n/a Summary This chapter summarizes the circuit implementation of the feed-forward op-amp and the class- AB OTA in the adaptive feedback network. The re-configurability is achieved using capacitor banks with MOS switches. The stability simulation results are studied and analyzed. All simulation results are presented and listed in a table.

77 CHAPTER 5. MEASUREMENT RESULTS 65 Chapter 5 Measurement Results This chapter summarizes the measurement results of the prototype TIA described in chapter 4. The PCB setup for transfer function and noise measurement are also shown. The measurement results compared to other published works are summarized and presented at the end of this chapter. 5.1 Test Setup The package chip is placed in a socket which is mounted on a printed circuit board (PCB) for measurements using laboratory equipment. The PCB is connected through a FPGA (National Instruments RIO USB-7856R) port which is controlled through LABVIEW interface on a Windows laptop computer. The input differential voltage signal is fed by a Vector Signal Generator through SMA connectors, and the differential output is connected to a Spectrum Analyzer through a differential probe Device Under Test The TIA prototype is fabricated with IBM 0.13μm CMOS technology. The active die area is about 0.45mm 2. The die photo is shown in Figure 5.1 with all the capacitors and amplifiers labelled. The chip has 32 pins and is packaged using QFN-32. The cavity of the package is about 5mm x 5mm. The dc supply and bias current of the chip is provided by the FPGA through a voltage regulator and tuned with potentiometer respectively.

78 CHAPTER 5. MEASUREMENT RESULTS 66 Cs Cs 700μm αc2 C1 OP OTA αc2 αc2 C1 αc2 C2 C2 C2 C2 680μm Figure 5.1: Chip Die Photo Printed Circuit Board A 4-layer printed circuit board (PCB) and a 2-layer PCB were fabricated to test the packaged chip. The 4-layer board has two signal layers, an internal power plane and an internal ground plane. The power plane is split into 4 VDD domains: one is for 5V from the FPGA port; one is for the chip VDD from the regulator; the other two are for external voltage supplies. The 2-layer board is for measuring noise with one op-amp, and an instrumentation op-amp. Figure 5.2 shows the block diagram of the PCBs and Figure 5.3 is the actual photo. A socket for the QFN-32 packaged chip is mounted on the 4-layer PCB. The VDD is provided by the voltage regulator and the bias currents are tuned with potentiometers. The four SMA connectors are for the differential input signals coming from the vector signal generator. They are used in pairs for measuring transfer function and linearity respectively. The input current is generated by feeding the signal with the voltage signal generator in series with a resistance of 1.6kΩ to emulate the finite output resistance of the passive mixer (as done in [6]). The output has two pins which are connected with a differential probe to the spectrum analyzer. For noise measurement, the output pins have to be connected to the other board, so the amplified noise signal is measured, due to

79 CHAPTER 5. MEASUREMENT RESULTS 67 the limitation of the instrument itself. With the probe, the noise floor level is higher than the noise floor level of the filter. FPGA Voltage Feedback Sensing Supply Voltage BIAS Generator Voltage Regulator Digital Control Signals Current Bias Supply Voltage Voltage to Current DUT Differential Input Signal (SMA) Differential Output Signal External Power Supply Supply Voltage Noise Measurement Circuit Differential Output Signal (Probe) Output Signal (SMA) Figure 5.2: Printed Circuit Board Block Diagram Figure 5.3: Printed Circuit Boards

80 CHAPTER 5. MEASUREMENT RESULTS Equipment Setup On the laptop computer connected to the National Instruments FPGA, a LABVIEW test bench has to be setup properly. All the biasing currents and chip total currents are measured with a small resistor, feeding back the voltages to the FPGA port. The voltages can be reported in currents on the LABVIEW GUI shown in Figure 5.4 simply by dividing the small resistor mounted on the board. All other digital control signals and reference common mode signal can be easily turned on/off on the GUI. The vector signal generator is set up properly to provide differential signals, and the two tones for linearity test. Figure 5.4: Graphic User Interface for Measurement with LABVIEW 5.2 TIA Measurement Results and Comparison This section presents the measurement results for the TIA prototype, focusing on the transfer function, input impedance, power, noise, two-tone test, large input signal test, and finally reported FOMs with different bandwidth and compared with the other published works Filter Transfer Function The filter transfer function is obtained shown in Figure 5.5 by measuring the gains with a small input current signal (i.e. 40uA), and the re-configurability is achieved by tuning the capacitive elements of the filter (including the input ground capacitance shown in Figure 5.4 as CS_CTRL). The frequency tuning range of the TIA measurement is between 2.8MHz and 12MHz to address cellular applications (i.e. WCDMA, and LTE20). The OTA is biased with 400μA in order to place the zeros one decade after the filter s cut-off frequency with a trans-conductance of 20mS