Low Cost AM/AM and AM/PM Distortion Measurement Using Distortion-to- Amplitude Transformations

Transcription

1 Low Cost AM/AM and AM/PM Distortion Measurement Using Distortion-to- Amplitude Transformations Shreyas Sen, Shyam Devarakond and Abhijit Chatterjee 2 Georgia Institute of Technology, Atlanta, GA, USA Student Member,IEEE, 2 Fellow,IEEE; {shreyas.sen, shyam, chat}@ece.gatech.edu Abstract Amplitude-to-amplitude (AM-AM) and amplitude-to-phase (AM-PM) distortion are two significant effects in power amplifiers at high output power levels. Traditional measurement of amplitude and phase distortion in RF power amplifiers requires the use of expensive vector network analyzers (VNAs). This paper proposes a low cost and accurate test methodology for AM-AM and AM-PM measurement using distortion-to-amplitude conversion using simple load board test circuitry along with the use of hardware and software based erence generation and peak detection mechanisms. It is seen that both distortion effects can be measured with high accuracy while allowing significant reduction in test cost.. Introduction The increased demand for spectrally efficient wireless communication chips necessitates the use of high linearity RF (Radio Frequency) front ends. Among other things, the High Power amplifier in the transmitter is a crucial element which determines the overall linearity of the transmitted RF signal. Power Amplifiers exhibit crucial distortion effects at high power namely amplitude and phase distortions. These are characterized as amplitude to amplitude modulation (AM-AM) and amplitude to phase modulation (AM PM). Moreover the increasing popularity of Orthogonal Frequency Division Multiplexing (OFDM) as the choice of modulation has increased the linearity requirements of these PAs significantly, making AM-AM and AM-PM even more critical. AM-AM distortion or gain compression causes intermodulation distortion (IMD) resulting in the folding of the out of band signal onto the desired signal spectrum, thereby resulting in higher bit error rate. AM-PM distortion or phase distortion causes unequal rotation in the received constellation causing iculties in signal detection. The sum effect of AM-AM and AM-PM causes bit errors at the received signal as well as out of band interference in the transmitted signal leading to violation of the defined FCC transmit spectral mask. There have been a number of techniques listed in prior literature which deal with modeling and compensation of AM-AM and AM-PM effects. These range from simple polynomial based models to complex models based on volterra series [] to model memory effects in PAs. In [2] the authors present a detailed comparative study of the traditional behavioral modeling methods for PA. [3] presents a detailed equation based modeling of the nonlinearities but conclude that non-linearity penalty at high powers is significant and not easy to reduce. They also propose that pre-distortion and compensation is the best way to deal with PA non linearities. This necessitates an accurate method for measuring these distortion effects. Amplitude distortion effects (AM-AM) are considerably less challenging to measure. Among other techniques, a simple technique such as placing a power detector at the PA output and measuring the output power level while sweeping the power of the input sine test signal can be used to measure gain compression. However accurate measurements of AM-PM effects require high precision instrumentation and hence are expensive, time consuming. The most common form of measuring AM-PM is using a Vector Network Analyzer (VNA). The measured phase of S2parameter in the swept power S parameter measurement provides the AM-PM information of the amplifier. Besides cost and time (setup time and calibration time) considerations in this particular setup, the measurement is highly sensitive to calibration. Hence, low cost test method for measuring AM-AM and AM-PM is desired for production testing solutions. [4] shows a low cost interesting jitter testing method which can be thought of as the digital counterpart of this analog problem. [5] uses jitter amplification through down conversion for accurate jitter measurements. In [6] authors develop an AM-AM and AM-PM method using unequal two tones. Another interesting test technique to measure AM-AM and AM-Pm simultaneously could be found in [7]. But they (like many others) do not provide a low-cost measurement solution. In this paper we concentrate on developing a truly low cost AM-AM and AM-PM measurement technique using only sine waves as test signals. The rest of the paper is organized as follows. Section 2 develops the basic theory for the low cost test method. Section 3 describes two alternative implementations of this technique and simulations results from them. Hardware implementations of one of the technique and measurement results are shown in section 4. Discussions and conclusion are presented in section 5. Paper 6.3 INTERNATIONAL TEST CONFERENCE /9/$ IEEE

2 2. Core Concepts This section develops the basic theory behind the proposed simplified phase distortion measurement technique and relies on the following observation: Key observation: The erence of two sine waves with identical amplitude and frequency but erent phase is another sine wave with the same frequency whose amplitude is proportional to the phase erence of the two sine waves. The following derivation proves the above observation, where ω is the frequency of the two sine waves, A is their amplitude, φ is the phase erence between them and V is the erence between the two waveforms. Assuming both of them as cosine waves we get (as also observed in [8]) V = Acos( ωt) Acos( ωt+ φ) = A[cos( ωt) cos( ωt)cos( φ) + sin( ωt)sin( φ)] = A[cos( ωt){ cos( φ)} + sin( ωt)sin( φ)] = 2Asin( φ 2) sin( ωt+ φ 2) () Similarly for sine waves it can be shown that V = Asin( ωt) Asin( ωt+ φ) = 2Asin( φ 2) cos( ωt+ φ 2) (2) In both the cases, it is found that V 2Asin( φ 2) = (3) i.e. the amplitude of the erence of the two waves is dependent on the phase erence of the original waveforms, more accurately, is proportional to the sin( ) of half of the phase erence between them. Figure shows this observation in graphical form. Figure a) shows a sine wave with zero phase and four other sine waves with increasing phase shift (φ =-, -3,-6 and -9). Figure b) shows the erence between the zero phase signal and the four signals with erent phase values. As derived in Equation (2), the erence between the waveforms is a cosine wave with same frequency, φ 2 phase delay (evident from the delayed zero crossing) and an amplitude given by 2Asin( φ 2) (since φ is negative, this term is positive). This key observation allows conversion of phase erence between two signals of identical frequency to amplitude and allows detection of phase deviation and distortion through low cost test techniques. The following sections describe how this property can be used to measure AM-AM and AM-PM distortions in RF PAs. a) Normalized Amplitude(a,b) Normalized Amplitude(V ) a=asin(ωt) and b=asin(ωt+φ) Normalized time(t) a=asin(ωt) and b=asin(ωt+φ) b) Normalized time(t) Figure : a) Asin( ωt) and Asin( ωt φ) φ=- φ=-3 φ=-6 φ=-9 V =Asin(ωt) - Asin(ωt+φ) φ=- φ=-3 φ=-6 φ= for erentφ. b) Difference wave showing amplitude proportional to the phase erence of the two waves in a). 3. Measurement of AM-AM and AM-PM Effects in Radio Frequency Power Amplifiers RF power amplifiers (PAs) are large signal devices that exhibit non linear effects with increasing input power. The important parameters that define the performance of an RF power amplifier are gain, phase deviation, -db compression point, amplitude-to-amplitude distortion (AM-AM distortion) and amplitude-to-phase distortion (AM-to-PM distortion). These are defined as follows [9]: Power Gain is the ratio of the output power delivered to the load of the power amplifier to the power available at the source of the amplifier. Phase deviation is the constant phase erence between the output of the PA and the input of PA due to the delay added by the PA circuitry. Gain Compression: With increasing input power levels the output power is progressively compressed and hence output power fails to increase linearly with input power. This reduction in gain is known as gain compression and is characterized by the db compression point (PdB) of the amplifier, i.e. the output power level for which the gain reduces by db from its small signal value. Paper 6.3 INTERNATIONAL TEST CONFERENCE 2

3 Figure 2: Block diagram of implementation using RF erence generator circuit AM-AM distortion defines the manner in which the amplitude of the PA output is affected by gain compression of the power amplifier input-output transfer function at high output power levels. AM-PM distortion defines the manner in which the phase of the output signal at a particular frequency is affected by nonidealities in the power amplifier input-output transfer function in relation to the phase of the signal at the same frequency that is input to the device. AM-AM distortion is defined as the change in gain per db increase of input power and characterized by db/db. Similarly AM-PM is defined as the phase change per db increase of input power and is expressed in degrees/db. The above specifications can be determined from gain and phase deviation measurements obtained by sweeping the PA input power across a range of values. The most common form of this measurement is performed using a vector network analyzer (VNA) and includes the following steps: ) Calibration of the VNA for the measurement setup. 2) Measurement of gain vs. input power. 3) Measurement of phase deviation vs. input power. In this section we propose two low cost test techniques for AM-AM and AM-PM distortion measurements that do not rely on the use of an expensive vector network analyzer (VNA). Traditional RF power amplifiers have a power detector (PD) at the output of the amplifier. Using this PD, low-cost measurement of gain compression is fairly straightforward. However, AM-PM distortion effects with increasing output power levels are icult to measure accurately without a VNA. This work addresses this problem using the core concepts described in Section 2. The key innovation is to first calibrate the AM-AM distortion effect out of the AM-PM distortion measurement procedure, then map the AM-PM distortion into amplitude variations of a erence signal as in figure and measure the amplitude using peak detection circuitry and software. Once the peak value of the erence signal is determined, the underlying AM-PM distortion of the RF PA device under test can be easily calculated. In the following sub-sections, the implementations of the two proposed test methods are described. 3. Using RF erence circuit This section describes how AM-AM and AM-PM distortion measurements can be performed directly in the RF domain using an amplitude equalizer (variable attenuator) and erence generator circuit (to perform phase-to-amplitude conversion). 3.. System Description Fig. 2 shows the test setup proposed for the low cost test technique. Fig 2a the shows setup for AM-AM distortion measurement. There are two steps in the test procedure. Step measures the Gain and AM-AM distortion effects of the PA. Step 2 uses data from Step to measure the AM-PM distortion of the PA. These are described below. Step : A controllable output power RF signal source is used to generate the RF sinusoidal input signal. A Wilkinson Power Divider (WPD) splits this signal into two signals with equal output power. One signal is used to drive the RF PA input and the other signal is used as a reference for distortion measurement. Commercial PAs (e.g. MAX 2242 []) generally have a power detector at the output. This can be used to measure the PA output power across erent input power levels. The erence between the output and input power (with the drop due to WPD accounted for) provides gain at lower power levels and gain compression (hence AM-AM) at higher power levels. Paper 6.3 INTERNATIONAL TEST CONFERENCE 3

4 Step 2: Fig 2b shows the AM-PM distortion measurement setup. The reference signal derived from the power divider output should be as clean as possible. If the reverse isolation of the power divider is not very high the reference signal contains unwanted noise and therefore careful attention should be paid to the reverse isolation spec of the power divider. An optional band pass filter at the RF test frequency can be used for generating a clean reference as shown in Figure 2. A variable attenuator is used at the output of the PA to equalize the power of the reference and the attenuated output. For each input power value a software actuated control mechanism sets this attenuation value as per the gain and AM-AM distortion values measured in Step. In case a BPF is used, its inputto-output power loss is used to modify the attenuation values of the attenuator so that the correct erence signal is produced at the output of the test setup. The variable attenuator ensures that the power of both the attenuated PA output and the reference is the same for all input power levels, thereby removing the AM-AM distortion effects. These two signals are then passed through a erence generator circuit (described later) which produces the erence signal V = Acos( ωt) Acos( ωt+ φ) as per Equation (). Finally, a peak detector measures V from which the phase shift φ using Equation (4) derived from Equation (3), for each power level concerned is obtained. φ = (4) sin ( V 2 A) The variable attenuation and the erence generator circuit are the key modules used in the proposed implementation. As described in Section 2 for V to be truly due to the phase shift introduced by AM-PM distortion, it is important that both the signals that are compared have the same amplitude. If this is not the case, V will be a function of the amplitude mismatch between the two signals and hence phase distortion prediction will be inaccurate. However, since the actual attenuation required is given by the gain specification at erent input power levels (obtained in Step ), the same can be controlled accurately by software. The erence generator circuit needs to be linear across the range of input signal power concerned. Any nonlinearity in this circuit can be characterized and the test procedure can be calibrated to achieve correct phase distortion measurement. The following flow graph summarizes the proposed test methodology. Step corresponds to the first block of Figure 3. Step 2 consists of the next two blocks of Figure 3. They are as described below: Step : Using built in RF power detectors measure the PA output power for range of input power concerned. This gives gain, gain compression and AM-AM. Figure 3: Methodology Step 2.: Using this information the attenuation value is set depending on the input power such that the amplitude of the reference (derived from input) and the PA output after attenuation is the same. This step removes the AM- AM effect from the PA output, but the phase deviation still remains. Step 2.2: Finally, a erence generator circuit generates a sinusoid whose amplitude is dependent (by Equation (3)) on the phase erence. Using Equation (4), the measured phase provides phase deviation and AM-PM distortion measurement RF PA Design Figure 4: PA circuit A two stage RF PA has been designed using CMOS.35u technology for simulation purposes. The simplified schematic for this PA is shown in figure 4. An input matching is provided before the driver stage so that maximum power could be transferred from the signal Paper 6.3 INTERNATIONAL TEST CONFERENCE 4

5 source. The driver stage was designed to provide a gain of around 3 db whereas the power stage was designed to deliver a gain of around 9 db at 2.4GHz. The driver stage and the power stage were connected through an inter-stage matching network of band pass type. Output matching is provided to match the output to 5 ohm. A harmonic termination network at the output provides good suppression at harmonic frequencies. The complete PA is designed from a 3.3V supply to have a gain of 2 db, output db compression point (PdB) of dbm and Power Added Efficiency (PAE) greater than 4%. This PA is used for both the methods for simulation purposes as well as for process and temperature simulations in section 3.4. The input PdB of the PA is around 6 dbm ( =5.92) Simulation Results This section describes step by step results for the measurement method in figure 2 and finally shows measurement accuracy over input power. Since the designed PA has an input PdB of 6 dbm the PA has been characterized with input RF power sweep from -2 dbm to dbm to cover both linear and compression region adequately. Vout,Vin (Volts) Vout,Vin (Volts) 5 Input and Output of PA PA output with increasing power -5 PA Input time(ns) Reference and Attenuated Output of PA Attenuated PA output with increasing power Reference with increasing power time(ns) Figure 5: a) Original PA output and Reference b) normalized PA out and reference Figure 5a shows the reference (equal to the PA input) and PA output for erent input power levels. The erence in the power levels is due to the gain of PA. Fig. 5b shows the attenuated PA output and the reference for several input power levels. It can be seen that the AM-AM effects have been removed accurately and the attenuated output and the reference have same amplitude for all the input power levels. If a constant attenuation (equal to the linear gain of the PA) were used then the PA output would have been lesser in amplitude than the reference for higher input power due to gain compression. a) Vout,Vin (Volts) Ref. Zero crossing time(ns) V (Volts) PA Output Zero crossing Peak of V (Volts) Difference Generator Output.5 Increasing power time(ns) Figure 6: a) Zoomed in version of fig 5b, showing phase distortion in RF out b) erence waveform V c) peak detector output V. Zoomed in version of 5b at zero crossing is shown in figure 6a. Zero crossing of the reference remains same for all input powers as expected. The erence in zero crossing is equivalent to the phase erence between the two waves. It is interesting to note that the changing zero crossing of the attenuated PA output reflects the actual phase distortion occurring in the PA as amplitude increases. This shows that the phase distortion is present before erence generation and hence we expect this to reflect inv.figure 6b and 6c show V (erence generator output) and V (peak detector output), respectively, for increasing input power levels. In Figure and 5b, the original two signals are cos( ωt) cos( ωt + φ) with φ negative. The erence signal in Figure 6b issin( ωt + φ 2) supporting Equation (). The amplitude of this erence signal is given by Equation (3). Hence using Equation (4), we get the phase deviation plot of Figure 7. The actual phase deviation obtained from circuit level simulation in Agilent ADS is plotted for comparison purposes. The measurement has an rms error of only.8% over the total input power range. Phase Deviation (degree) b) c) Measured Phase Deviation Original Phase Deviation Figure 7: Original and measured phase deviation Paper 6.3 INTERNATIONAL TEST CONFERENCE 5

6 The AM-AM distortion measured and the AM-PM distortion derived from phase measurements are plotted in Figures 8a and 8b, respectively. The AM-PM measurement shows rms error of only 5.8 %. Next, we consider the design of erence generator circuit for practical implementation of this RF measurement system. AM-AM (db/db) AM-AM Figure 8: a) Measured AM-AM b) Measured and actual AM-PM 3..4 Difference Generator Circuit design The most critical non-standard block in this method is a erence generator circuit that generates the erence between two input RF signals of identical frequency. Hence the challenge is to design a erence amplifier with the following properties: ) The output is proportional to the erence of the two input signals. 2) The erence generator should have wide bandwidth as both inputs and outputs are of RF frequency. 3) It should be as linear as possible for the input range concerned. Figure 9: Simplified schematic of erence generator circuit A simplified schematic of the implementation of such a erence generator circuit is shown in Figure 9. A resistive loaded common source amplifier is used for this purpose. DC biasing is provided through inductors (L) at both gate and source, whereas the RF input signals are AC A M -PM (degree/db) AM-PM original measured -2 - coupled through capacitors(c). R bias sets the current through the device as well as the gain. The AC coupled output is equal to V as per Equation () if the inputs are given byv in = Asin( ωt) and V in2 = Asin( ωt+ φ). The gain (G) of the circuit would adds a scaling factor to V which is accounted for by modifying (4) as φ = sin ( V 2 AG) (5) The RF input port (V in ) is matched to 5 ohm to match the PA output impedance. The other input port (V in2 ) is a high impedance input which samples the signal from a 5 ohm termination on the reference signal path. The output voltage is proportional to the phase erence between the two inputs as can be seen from the following figure. It shows V with φ for several values of the input power concerned. It also shows that the design behaves very linearly from RF power levels from -2 dbm to 7 dbm for phase shifts up to even 6 degrees. For smaller phase shift values it is linear even at higher input power levels. max of V Figure : Difference Generator Output φ (degree) V RFin=7 dbm RFin=-2 dbm for increasing φ for erent input power 3..5 Drawbacks and Limitations The concerns with this approach are as follows: ) The method needs a high frequency linear erence generator circuit, which might be hard to design depending on the power levels required. 2) The peak detectors used should also be linear with input power. In case they are non-linear the methodology needs to be calibrated using the known non-linearity. 3) Finally, any gain and phase mismatch in the two paths in figure b would introduce errors in measurement. This requires either one time careful design of the load-board or calibration for the gain and phase offset. Paper 6.3 INTERNATIONAL TEST CONFERENCE 6

7 DUT Fixed Attenuator Linear Mixer Sampler SOFTWARE A/D Wilkinson Power Divider Power Splitter Difference Generator RF Source LO Sampler A/D Band Pass Filter (optional) Linear Mixer Figure : Block diagram of method using down conversion and sampling 3.2 Distortion Measurement Using Down Conversion and Sampling This section describes an alternative implementation of the low cost measurement method without using a high frequency erence generator or a variable attenuator. Using down conversion and sampling of the high frequency signals this implementation performs the amplitude equalization and erence generation in software System Description Figure shows the block diagram of the measurement setup. A variable output power RF source is used to generate the input signal. It is then divided into two equal parts using a Wilkinson power divider, one of which is used as the PA input whereas the other is used as reference signal. An optional band pass filter can be used to increase the purity of the reference as described in Section 3... A fixed attenuator with attenuation equal to the nominal linear gain of the PA is used instead of a variable attenuator. This allows both the attenuated PA output and reference to be at similar power levels, but does not remove AM-AM distortion effect from the attenuated output. Two matched linear down conversion mixers are used to down convert both the attenuated PA output and the reference to low frequency signals (5 MHz in our case). A single RF source is used as the Local Oscillator (LO) signal of both the mixers by dividing it using a power splitter (WPD). Two matched analog-to-digital converters (ADCs) are used to sample these signals. The sampled signals have the same frequency but their amplitude er at higher power levels due to gain compression. The amplitude equalizer block performs the following operations:. Equalize the amplitude of the down converted PA output and reference for the lowest input power level. Since at lower input power, the PA does not exhibit gain compression and the attenuator attenuates by the same amount (linear gain of a nominal PA) ideally there should not be any amplitude erence between the two signals being compared. Any amplitude mismatch at this input power level reflects the amplitude mismatch in both the signal paths (path of reference signal, path of signal through DUT) arising from the presence of a non-nominal PA, non exact attenuation, non-matched mixers and ADCs. This mismatch is constant across all power levels and hence, if any mismatch exist all the down converted PA outputs should be equalized for the respective amount of power gain or loss. This removes any amplitude mismatch arising from all effects except gain compression. After this step, the signals corresponding to lower input power levels for which the PA does not exhibit gain compression have equal amplitude and so do the corresponding down converted signals for the same RF input signal power. 2. There is still residual amplitude erences present between the two signals being compared for higher input power levels due to AM-AM distortion effects. In this step these are equalized digitally and as a by-product, the amount of the equalization at each power level corresponds to the gain compression at that input power value. Hence, the outputs of the Equalize Amplitude block are two signals with no amplitude erence (phase erence still preserved) and the gain compression information of the PA over all power levels. The gain of the PA can be written as: Gain of PA = Attenuation of fixed attenuator (linear gain of nominal PA) + power equalization amount in step (dbs, gain erence due to non-nominal PA, constant over all power levels) + power equalization amount in step Paper 6.3 INTERNATIONAL TEST CONFERENCE 7

8 2 (dbs, erent for erent power levels in the compression region). (5) The above formula assumes that the mixers and ADCs are properly matched. Next, we analyze the erence between the two outputs from the Equalize Amplitude block. The erence signal is V and its amplitude is proportional to the phase erence of the two input signals as described in section 2 and 3... Application of Equation (4) in the Peak to Phase Conversion block, on this data provides the phase deviation between the signals being compared at all input power levels. The method proposed in this section uses the fact [5,- 2] that phase deviation is preserved by frequency translation and provides accurate phase information as long as the mixers are operating in the linear range of input power concerned. Another issue is the amount of attenuation to be programmed in the fixed attenuator. We suggest it should be set to be the same as the linear expected gain of the PA DUT (in dbs). In case the attenuation is not exact, Step of the procedure outlined earlier for operation of the Equalize Amplitude block compensates for any subsequent amplitude mismatch effects. The main purpose of this attenuator is to ensure that both the signals being compared are in the same power range so that the dynamic range requirements of components of devices in both the reference signal and DUT signal paths are the same and hence, matched mixers and ADCs can be used Results This section describes the measurement results for the down conversion and sampling method described above. The down converted signals are of 5 MHz as can be observed from figure 2. This plots show the signals after step in the Equalize Amplitude block in figure. PAout, Ref (Volts) Downconverted Reference and PA Output Gain Compression Down converted PA output Down converted Reference time(ns) Figure 2: Down converted PA output and reference Gain (db) Gain Compression Figure 3: Gain compression measured and original The output has same amplitude as the reference for lower power levels, whereas, for higher powers it exhibits gain compression as pointed out in the figure above. This lets us measure AM-AM in step 2 as described earlier. In figure 3, the measured gain values using equation (5) are plotted along with the original gain values obtained from circuit level simulation in Agilent ADS over the input power range concerned. The gain measurement turns out be very accurate with only.3% rms error over all power levels. The waveforms also have the phase erence information in them. Using (3) and (4) the phase is measured and is shown in figure 4 along with original phase deviation. Phase measurement using this method produces an rms error of.22%. Phase Deviation (degree) Phase Deviation Measured Phase deviation Deviation Measured Original Phase Deviation deviation RF input power (dbm) Figure 4: Phase deviation measured and original A gilbert cell mixer with source degeneration and single to erential end conversion was used as the down conversion mixer for simulation purposes. This mixer had an input db compression point of 5dBm, i.e. the mixer was not linear enough. The slight deviation of the measured phase from actual at higher power levels is due to the compression of the mixer at these power levels. With a more linear mixer (which is readily available as off the shelf component) measurement accuracy would further increase. Another point to note is the output leads the reference in phase in figure 2. This is caused as both the down conversion mixers are inverting. But this does not affect measurement accuracy. Paper 6.3 INTERNATIONAL TEST CONFERENCE 8

9 AM-AM (db/db) Figure 5: a) Measured AM-AM b) Measured and actual AM- PM The AM-AM and AM-PM derived from the measurements above are plotted in figure 5 along with their actual values. They exhibit an rms measurement error of % and 4.74% respectively Discussions or Limitations This method uses two matched mixers and samplers. Hence any nonlinearity of these get cancelled out by subtraction in the software. But like the previous method both the paths should be either matched or calibrated for. The main drawback of this method is the requirement of two RF signal source instead of one. 3.3 Measurement over Process and Temperature Measured values (normalized) AM-AM original measured Figure 6: Scatter plot of normalized gain and normalized phase over Process and Temperature To ascertain the accuracy of the proposed low cost test method several process and temperature instances of the PA were generated using Monte-Carlo and parametric simulations. The gain and phase of each of those instances are measured using the method described above and the normalized values of those specs are plotted with normalized actual values. A low rms error (.58%) over all instances proves the accuracy of the proposed method. 3.4 Comparative Study AM-PM (degree/db) This section shows the comparative study of the two implementations proposed in a tabular form..5.5 AM-PM original measured -2 - Gain and Phase Measurement over process and temperature.5.5 Actual Values (normalized) Method Using RF erence Circuit Using Down Conversion and sampling Table : Comparison of two proposed methods Hardware required 2 WPD, RF source, Power Detector, Variable Attenuator 2 WPD, 2 mixers, 2 ADC, 2 RF source 4. Hardware Validation 4. Experimental Setup WPD at LO divider Matched Mixers Two Low Freq output Pros Only RF source Nonlinearities cancel out Attenuator Amplifier (DUT) Cons Design of RF erence circuit WPD at RF input More hardware required Figure 7: Experimental setup with components marked RFin This section describes hardware implementation of the proposed low cost AM-AM and AM-PM measurement methodology. Agilent E8363 PNA has been used to measure the accurate gain and phase distortion of DUT. Due to limited power sweep capabilities of the PNA used we are using a low power amplifier as DUT. The setup shown in figure has been recreated in hardware as shown in figure 7. The variable power RF input of 8 MHz from Agilent E4432B (signal generator) is divided in two equal parts using a custom designed WPD. One output is passed through the amplifier DUT (RF24) and attenuated (fixed attenuation) before feeding to one of the two matched mixers (MAX239). The other WPD output goes directly to the other mixer and acts as a reference. Both the LOs (82 MHz) are generated from HP 8648D RF signal source using a second WPD. The two down converted low frequency signals are sampled by two parallel channels of AlazarTech (ATS46) sampler ADCs. The sampled data is processed in Matlab in a PC to generate final measurement results. Figure 8 shows both the low frequency ( MHz) waveforms at the onset of amplifier (DUT) saturation in the AlcazarTech Sampler interface. Paper 6.3 INTERNATIONAL TEST CONFERENCE 9

10 Figure 8: Captured downconverted signals at onset of amplifier saturation using AlazarTech Sampler 4.2 Experimental Results This section presents the measurement results derived from the experimental setup described in previous section using formulas in section 3. The gain and phase measurements for both VNA and proposed low cost AM- AM and AM-PM measurement method using down conversion and sampling are plotted in figure 9 and 2, respectively. The results have been calibrated to remove phase and gain offset created by the mismatch in the two paths. Both gain and phase measurement show good correlation (.72% and 2.3 % rms error respectively) with the actual values measured from VNA over erent input powers proving the validity of the proposed method. Gain (db) Figure 9: Gain measured using VNA and proposed method Phase Deviation (degree) Gain Measurement original from VNA proposed low cost method Phase Measurement original from VNA proposed low cost method Figure 2: Phase measured using VNA and proposed method 5. Conclusion and Future Work Traditionally, AM-AM and AM-PM measurements are performed using expensive vector network analyzers (VNAs). This paper proposes a low cost AM-AM and AM-PM measurement technique based on distortion to amplitude transformations. The theory along with two implementations has been proposed. Hardware experiment results show that both distortion effects can be measured with high accuracy while allowing significant reduction in test cost. Future work would involve extending this technique to measure IQ imbalance in RF front ends as well as the extensive study of amplitude and phase mismatch on this method. 6. Acknowledgement This work was funded by GSRC/FCRP 23-DT References [] Zhu, A.; Brazil, T.J., Behavioral modeling of RF power amplifiers based on pruned volterra series, IEEE Microwave and Wireless Components Letters, Volume 4, Issue 2, Dec. 24 Page(s): [2] Magnus Isaksson, David Wisell, and Daniel Rönnow, A Comparative Analysis of Behavioral Models for RF Power Amplifiers, IEEE Transactions On Microwave Theory And Techniques, Vol. 54, No., January 26, Pp: [3] S. Pupolin et al. Performance Analysis of Digital Radio Links with Nonlinear Transmit Amplifiers, IEEE Journal on Selected Areas In Communications, Vol. 5, No. 3, April 987 pp: [4] Yamaguchi, T.J., et al., A New Method for Measuring Aperture Jitter in ADC Output and Its Application to ENOB Testing, IEEE International Test Conference, Oct. 28 Page(s): 9 [5] Hyun Choi, Donghoon Han, Chatterjee, A., Enhanced Resolution Jitter Testing Using Jitter Expansion, IEEE VLSI Test Symposium, May 27 pp:4 9. [6] Campbell, C.F., Brown, S.A, Application of the unequal two-tone method for AM-AM and AM-PM characterization of MMIC power amplifiers, 2 IEEE Emerging Technologies Symposium on Broadband Communications for the Internet Era, - Sept. 2 Page(s):3 6. [7] Ghannouchi, M., Guoxiang Zhao, Beauregard, F., Simultaneous AM-AM/AM-PM distortion measurements of microwave transistors using active load-pull and six-port techniques, IEEE Transaction on Microwave Theory and Techniques, Volume 43, Issue 7, July 95 Pp: [8] E. Acar and S. Ozev and K. Redmond, A Low-Cost RF MIMO Test Method Using a Single Measurement Set-up, 25th IEEE VLSI Test Symposium, 27. Pages: 3-8. [9] Behzad Razavi, RF microelectronics, Prentice-Hall, Inc., Upper Saddle River, NJ, 998. [] [] T. J. Yamaguchi, M. Ishida and M. soma, A Wideband Low-Noise ATE-based Method for Measuring Jitter in GHz Signals, Int. Test Conf., 8- Nov. 25. [2] T. J. Yamaguchi, M. Soma, D. Halter, R. Raina, J. Nissen and M. Ishida, A Method for Measuring the Cycle-to-Cycle Period Jitter of High-Frequency Clock Signals, VLSI Test Symp., 29 April - 3 May 2, pp. 2-. Paper 6.3 INTERNATIONAL TEST CONFERENCE