DESIGN OF A FULLY DIFFERENTIAL HIGH-SPEED HIGH-PRECISION AMPLIFIER Mayank Gupta mayank@ee.ucla.edu N. V. Girish envy@ee.ucla.edu Design I. Design II. University of California, Los Angeles EE215A Term Project Report Professor B. Razavi, Fall 2001 Abstract: We have designed a fully differential high-speed high-precision amplifier with a fixed gain of 8. Our two design criterion were that of (a) using a power budget of 20mW minimizing the settling time and (b) to target a 0.5% large-signal settling time of 20ns, with the aim to minimize the power consumption. Our Circuit achieves a differential output swing of 2Volts, with a power supply of 3V. Internally the amplifier is a foldedcascode stage and uses common mode feedback, to stabilize the output. Simulation with Cadence Spectre have been included in the term report.
I. Design Description and Overview The design required that two versions of a fully differential high-precision amplifier be made with the aim of minimizing the power consumption and minimizing the settling time. The specifications that both versions had to satisfy are given below: Supply (V dd ) 3V Gain 8 Differential Output Swing 2V Load Capacitance 1pF Gain Error 1% Settling Accuracy 0.5% Power Dissipation 20mW Settling time Minimum Table 1: Design Specifications 1 Supply (V dd ) 3V Gain 8 Differential Output Swing 2V Load Capacitance 1pF Gain Error 1% Settling Accuracy 0.5% Power Dissipation Minimum Settling time 20ns Table 2: Design Specification 2 In order to get a gain of 8, a capacitive feedback network has been used. This configuration is shown below: Figure 1: Amplifier with feedback network II. Topology Selection The first step in designing the amplifier is to choose a stage that could provide the appropriate gain. Since the gain error was specified as 1%, we calculate the open loop gain of the amplifier as follows: Vout Gain + 1 = Gain 1 + =8 Vin Openloop _ Gain This implies that the open loop gain should be roughly 900, which is of the order of (g m r o ) 2. Keeping this in mind we can get this level of gain from a single Cascode or Telescopic stage. The voltage swing in a Telescopic stage is limited to 2[V DD - (2*PMOS Overdrives + 3*NMOS Overdrives)] and as the design constraints specify a output differential swing of 2 Volts, we chose a Folded Cascode topology. In order to make the output common mode level more stable to voltage fluctuations, common mode feedback was used to fix the input and output common mode voltage to V DD /2. The circuit topology used in the design is shown in the next page and the various design tradeoffs will be discussed in the succeeding sections.
III. Design Trade-Offs In both the design approaches the following tradeoffs were observed: (a) The CM feedback transistors M12 and M13 always introduced some parasitic capacitances, reducing the gain and bandwidth of the op-amp. (b) Since the CM voltage was set to 1.5Volts, the overdrive of the transistors M5, M6, M1, M2, M11, M12 and M13 was constrained. This precondition forced these transistors to have relatively higher widths than the rest of the transistors in the circuit. This problem was very exaggerated for the case of M12 and M13 since they had to be operated in deep triode region, with low over drives and their widths could not be increased beyond a certain limit since it lowered the output impedance of the Op-Amp. Figure 2: Amplifier Topology with common mode feedback
Figure 3. Biasing Circuit with parasitics Both the design approaches used the above circuit-biasing network. This circuit also includes the various parasitics associated with the feedback, load and input capacitors. IV. Realization of Design Target 1: Maximum Power Usage (20mw) with aim to Minimize the Settling Time. With a total allowed current of 6.6mAmp, the circuit was designed to have the least settling time possible. The circuit had an Open Loop gain of 1.385K and a Bandwidth of 2.893Mhz. The device sizes and the other related values for our final design are as given below. Differential Amplifier Description: Device Description Type W/L(µm/µm) Current(µA) g m (ms) r o Ω M0 Reference for Common Mode Feedback N 10.88/0.5 100 0.15 605.4 M1,M2 Input Differential pair N 449/1 1457 11.38 1524.8 M3,M4 PMOS Cascode Devices P 415.2/1 1500 7.04 710.3 M5,M6 Current Sources for the folded cascode P 452/0.5 2957 16.91 146.5 M7,M8 NMOS Upper Cascode Loads N 126.36/1 1500 5.88 746 M9,M10 NMOS Lower Cascode Loads N 88.43/0.5 1500 8.01 254.8 M11 Tail Current Source for Input Differential Pair N 298.68/0.5 2914 20.32 98.3 M12,M13 Common Mode Feedback Pair N 163/0.5 1457 2.16 40.2 Mb1 Bias reference & mirror for M11 N 8.96/0.5 100 0.70 11032 Mb2 Bias reference & mirror for M5, M6 P 40.6/0.5 100 0.57 11996 Mb3 Bias reference & mirror for M9, M10 N 5.1/0.5 100 0.53 11743
The values of the various capacitances and resistors used for this configuration where as follows Feedback Circuit: Device Description Values C1, C2 Input Capacitance 7.2pF C3, C4 Feedback Capacitance 0.9pF C par1, C par2 Parasitic Capacitance 1.44pF C par3, C par4 Parasitic Capacitance 180f F C load Load Capacitance 1pF R1, R2 Feedback resistors 1GΩ Under these device values the circuit had the following specifications for DC bias V reference =1.5V V out1 =V out2 =1.501V Vb1=1.8V Vb2=1.15V Differential Output Swing =2V Gain Error= 0.97% Settling time =7.26nS Power consumed = 19mW V. Realization of Design Target 2: 0.5% Settling time (20ns) with Minimum Power Dissipation The folded cascode differential amplifier topology (Figure 2) was used to achieve this design to minimize the power dissipation and limit the settling time to 20ns. The device dimensions, currents and bias voltages were chosen to give a high open loop ac gain so as to achieve the gain error specification (Gain Error<1%). The differential amplifier was then embedded in a closed loop feedback circuit as shown in Figure 3 and the differential output was simulated to achieve the settling time specification for maximum output swing (2V). Differential Amplifier Description: Device Description Type W/L(µm/µm) Current(µA) g m (ms) r o Ω M0 N 5.86/0.5 100 0.156 1.16K Reference for Common Mode Feedback M1,M2 Input Differential pair N 117.54/0.5 303.45 each 4.75 6.42K M3,M4 PMOS Cascode Devices P 127.61/0.5 332 each 3.17 2.70K M5,M6 Current Sources for the folded cascode P 111.6/1 635.4 each 2.32 0.948K M7,M8 NMOS Upper Cascode Loads N 10/0.5 332 each 1.35 3.32K M9,M10 NMOS Lower Cascode Loads N 81.6/1 332 each 2.2 1.19K M11 Tail Current Source for Input Differential Pair N 65.3/0.5 606.9 4.36 0.55K M12,M13 Common Mode Feedback Pair N 17.77/0.5 303.45 each 0.47 0.38K Mb1 Bias reference & mirror for M11 N 9.32/0.5 100 0.72 11.14K Mb2 Bias reference & mirror for M5, M6 P 16.34/1 100 0.36 13.96K Mb3 Bias reference & mirror for M9, M10 N 23.3/1 100 0.65 11.06K
Additional Design Tradeoffs: In the process of the design to achieve the required specifications, the following tradeoffs were observed in addition to the ones discussed above: Power Dissipation vs. Device Dimensions: As the power dissipation was increased, the settling time correspondingly decreased, but at the expense of introduction of device capacitances which arose because of the need to increase the gain in order to decrease the gain error. Settling Time vs. Device Dimensions vs. Gain: To increase the gain, device dimensions of input differential pair (M1, M2), cascode current sources (M5, M6) and the loads (M7, M8, M9, M10) were increased. This increased the gain but also increased the settling time due to introduction of device capacitances at the output. Gain vs. Input Impedance: Increase in the device dimensions of the input differential pair devices increased the gain and also the input capacitance, thus reducing the input impedance. Figure 6 shows the open loop ac gain magnitude and phase response of the differential amplifier. Figure 7 shows the 0.5% settling time of 20ns with minimum power dissipation. Feedback Circuit: Figure 3 shows the feedback topology used for the design. The component values are given in the following table. Device Description Values C1, C2 Input Capacitance 2.4pF C3, C4 Feedback Capacitance 0.3pF C par1, C par2 Parasitic Capacitance 0.48pF C par3, C par4 Parasitic Capacitance 60fF C load Load Capacitance 1pF R1, R2 Feedback resistors 1GΩ For the differential amplifier and the feedback circuit, the DC bias conditions are as follows: V reference =1.5V V out1 =V out2 =1.5V Vb1=1.8V Vb2=1.15V Differential Output Swing =2V Gain Error= 0.995% Settling time =20.1nS Minimum Power Dissipation achieved = 4.71mW VI. Simulation Procedure used for both designs: Open Loop AC response: The input to the differential pair was given as a combination of a DC source with a CM level of 1.5V in addition to a sinusoid of amplitude 1V. The sinusoids applied to the 2 inputs were 180 degrees out of phase. Settling time: Two pulses of amplitude 0.125 and 0.125 volts (with rise time=fall time=0.1ns, pulse width=1µs, period=2µs) were applied to the non-inverting and inverting terminal of the feedback circuit respectively with the initial condition at Vout1=2V and Vout2=1V. The difference Vout2-Vout1 was then plotted versus time to observe the settling time. References [1] B.Razavi, Design of Analog CMOS Integrated Circuits, McGraw-Hill 2001 [2] S.Rabii and B.A. Wooley, A 1.8V Digital-Audio Sigma-Delta Modulator in 0.8-µm CMOS, IEEE J. of Solid-State Circuits,vol.32,pp. 783-796,June 1997.
Figure 4. Magnitude and Phase response for Design I. Power =19.5mW Settling Time=7.2nS
Figure 5. Transient response for Design I. Power =19.5mW Settling Time=7.2nS
Figure 6. Magnitude and Phase response for Design II. Power =4.71mW Settling Time=20.1nS
Figure 7. Magnitude and Phase response for Design II. Power =4.71mW Settling Time=20.1nS