Design Considerations in the
`Microwave Transition Analyzer
`
`Digital signal processing is used extensively to improve the performance
`of the microwave sampler, the sample-rate synthesizer, and the
`high-speed analog-to-digital converter, and to extract and display input
`signal characteristics in both the time domain and the frequency domain.
`
`by Michael Dethlefsen and John A. Wendler
`
`The HP 71500A microwave transition analyzer is an MMS
`(Modular Measurement System) instrument. As shown in
`the idealized block diagram, Fig. 1, it consists of the
`HP 70820A microwave transition analyzer module and the
`HP 70004A MMS mainframe and color display. For an
`explanation of the capabilities and applications of the
`microwave transition analyzer, see the article on page 48.
`
`The block diagram is relatively straightforward. The two
`input signals are sampled by microwave sample-and-hold
`circuits with an input bandwidth of 40 GHz. The sample rate
`is generated by a low-frequen~y 10-to-20-MHz synthesizer
`under processor control. The sampled signals are digitized
`by an analog-to-digital converter (ADC), the digitized outputs
`are processed by the digital signal processor, and the final
`results are displayed on the MMS display by the instrument
`processor.
`
`The implementation was somewhat more complex than it
`might appear from the block diagram. While microwave
`samplers with bandwidths up to 40 GHz were generally
`available, they were not designed to be used as sample-and(cid:173)
`hold circuits operating at rates up to 20 MHz. Low-frequency
`synthesizers, while also commonly available, did not have
`
`the desired phase noise performance. The available high(cid:173)
`speed ADCs, if used directly on the sampler output, would
`have been the primary noise floor and dynamic range limita(cid:173)
`tion of the instrument because of their limited resolution.
`Digital signal processing is relied upon heavily to achieve
`and improve much of the basic hardware performance and
`to extract and display the input signals' characteristics in
`both the time and frequency domains. However, the general(cid:173)
`purpose digital signal processors could not do a sigii.ificant
`amount of real-time processing at the 20-MHz data rates, so
`a large buffer memory was required between the ADC and
`the digital signal processor.
`
`This article attempts to explain some of the design consider(cid:173)
`ations, in both the hardware and the firmware, that went
`into the development of the microwave transition analyzer
`block diagram.
`
`Sampler Operation
`Microwave samplers have been used in RF and microwave .
`instrumentation for several decades.1 They traditionally
`have been the most economical way to obtain the broadest
`frequency coverage with the smoothest frequency response.
`
`I
`CH1 ~~--
`
`l
`GHz I
`
`Inputs
`DCto40
`
`:
`: Hold Circuits
`
`I
`I
`
`~ MSIB ~
`---
`-----
`----- 0 ---
`---
`-----
`
`HP 70004A MMS
`Display and Mainframe
`
`CH2 -+of o-r : *
`
`I
`
`10-MHz
`Reference --+----0
`
`10MHz
`
`HP 70820A Microwave Transition Analyzer Modula
`
`Fig. 1. Idealized block diagram of the
`HP 71500A microwave transition
`analyzer.
`
`October 1992 Hewlett-Packard Journal
`
`63
`
`RPX-Farmwald Ex. 1036, p 1
`
`

`
`Sampler Chip A
`J;
`
`IF Out
`
`100MO
`
`10 to 20 MHz from
`Frequency Synthesizer
`
`Step Recovery
`Diode
`
`To Second Channel
`
`Their noise figure is relatively poor. Their inherent broad(cid:173)
`band coverage has encouraged their use in frequency acquisi(cid:173)
`tion and phase-lock loops as well. However, their ability to
`capture the time-domain waveform (or the frequency-domain
`equivalent-simultaneously translating all the harmonics o(
`a repetitive waveform) is what made them so suitable for
`the 70820A.
`
`The basic concept of a microwave sampler is to generate a
`vecy narrow sampling pulse that turns on a series switch
`between the RF input signal and the IF circuitry, which is
`mainly a holding capacitor. The amount of time that the
`switch is on establishes the frequency response of the sam(cid:173)
`pler. If the switch is fully on for 10 ps, the ideal frequency
`response would be sinc(10-11f), which has a 3-dB bandwidth
`of 44 GHz. Although this assumption of a perfectly rectangu(cid:173)
`lar switch on-resistance as a function of time is only an ideal,
`it is a good enough engineering approximation to use here.
`As shown in Fig. 2, the series switch used in this sampler is
`an integrated pair of Ga.As diodes. The switching waveform
`is generated by driving a silicon step recovery diode at a
`variable sample rate between 10 and 20 MHz. The step out(cid:173)
`put of the step recovery diode is split into two signals, one
`for each channel. The sampler assembly then shapes and
`differentiates this edge to form a narrow impulse, which
`briefly turns on the diode switch, allowing some of the RF
`current to flow into the holding capacitor.
`
`For ideal sample-and-hold circuit operation, the output volt(cid:173)
`age should only depend on the input voltage during a single
`sampling instant. Its voltage should not depend on any pre(cid:173)
`vious samples or how often the samples are taken. There are
`two general techniques to achieve this sample-to-sample
`independence. One is to discharge the holding capacitor
`fully before each sample and measure the amount of charge
`or voltage on the hold capacitor after each sample. The
`other technique is to require that the sample-and-hold circuit
`
`64 October 1992 Hewlett-Packard Journal
`
`Fig. 2. Simplified diagram of the
`microwave sampler circuit.
`
`capacitor charge to 100 percent of the input voltage during
`each sample period. The limitations of using the microwave
`sampler as a high-speed, conventional sample-and-hold cir(cid:173)
`cuit now begin to become apparent. At the fast 20-MHz sam(cid:173)
`ple rates required, it is not possible to discharge the hold
`capacitor accurately before each sample. On the other hand,
`to attain .the required microwave input bandwidth, the sam(cid:173)
`pling pulse must be so narrow that it is not possible to
`charge the hold capacitor fully.
`
`A simplified model of a sample-and-hold circuit and the
`equations describing its frequency-domain transfer function
`are shown in Fig. 3. The fraction of the input signal that is
`stored on the hold capacitor is referred to as the sampler
`efficiency E, and for this model it can be computed as:
`
`R
`Yinls) ~1 .__ .... " " ' - - - - -- - -- - --
`I
`I
`
`Rp
`(»R)
`
`Voutls,S)
`
`s=jro
`Original Frequency (ro=23dl
`
`S=s-jNro5
`Down-Converted Frequency
`(ros=2ms=2n/ts)
`
`V out(s, S)
`(1 - E )e -stan)
`(1 -
`(1 - Be - sts) ·
`G(s S) = - - - = -----"----'----- - - - - - -
`ts(S + R \) (1 - 8(1 - E )e - sts)
`(1 + sRC)
`Vin(s)
`,
`p
`
`B = e - ts/RpC
`Hold Efficiency
`
`Fig. 3. Sampler model.
`
`E = 1 - e-•on/RC
`Sampler Efficiency
`
`RPX-Farmwald Ex. 1036, p 2
`
`

`
`1\ 1
`/1
`I
`I
`Vout ~ E=1
`V,m I
`
`ls
`
`2ts
`
`3ts
`
`4ts
`
`5ts
`
`&ts
`
`Vin
`
`Vout
`Ideal
`
`8:0.7
`
`E=0.25
`8=1
`
`frequency and the sampler efficiency as shown in Fig. 5. To
`solve this latter problem, the HP 70820A microwave transi(cid:173)
`tion analyzer module uses a very high-impedance buffer on
`the output of the sampler and provides a positive feedback
`bootstrap voltage to remove the low-frequency loading
`effects of the current biasing resistors as shown in Fig. 2.
`Operating with this high load impedance has the additional
`benefit of minimizing the sampler compression at high input
`levels since very little signal current has to flow through the
`sampler diodes. In a9dition, since the sampler diodes are
`effectively current biased instead of voltage biased, their
`sensitivity to temperature variations is considerably reduced.
`
`The problems created by the sampler low-pass filter effect
`are more difficult to solve. As the sampling frequency is var(cid:173)
`ied, the current bias is changed by the processor to keep. the
`sampler on-time t 0 n constant. This is required so that the RF
`frequency response does not vary noticeably with sampling
`frequency. However, since the sampler time constant is pro(cid:173)
`portional to t 0 nlts, the IF bandwidth now varies with sam(cid:173)
`pling frequency. To solve this problem a programmable zero
`was added following the IF buffer amplifier (see Fig. 7).
`During the IF calibration process, the sample-and-hold cir(cid:173)
`cuit low-pass pole is measured as a function of the sampling
`frequency. Whenever the sampling frequency is changed, the
`programmable-zero amplifier is adjusted to cancel the effect
`of the sampler pole.
`
`Another challenge encountered when using a microwave
`sampler as a sample-and-hold circuit is its feedthrough capac(cid:173)
`itance. A capacitance as low as 50 femtofarads between the
`RF input and IF output will cause significant errors in the
`expected operation of the microwave sampler. Signals be(cid:173)
`low 10 MHz will directly couple into the IF even when the
`sampler is supposed to be off. To cancel this effect, the input
`signal is tapped off before the sampler diodes, inverted, and
`capacitively summed back into the IF signal.
`
`The IF output of the sampler is ac coupled. When the instru(cid:173)
`ment is de coupled, the de component is restored .by picking
`it off before the sampler diodes and summing it back in at
`the IF buffer stage. The crossover frequency is about 3 Hz.
`
`Od8
`
`-r---.
`r--. ·
`
`8: O.!
`
`I' rr
`
`8=09
`
`-r---. " ....
`
`~,...I"'~
`
`- ~ i : 1
`-,...._ ;-..., '\
`...
`
`'\
`
`~
`
`~ "
`"
`
`~r-1==~
`
`~
`i: = D
`'
`I\
`:-..
`
`I\~
`
`N ~· c ~E~
`
`'\I\
`
`l\E ~1
`\ I
`' I '
`
`"""
`
`~
`'
`
`-50d8
`
`I"
`
`r
`
`'
`
`I
`
`Fig. 5. Sampler IF frequency response for different values of
`sampler efficiency e and hold efficiency B.
`
`October 1992 Hewlett-Packard Journal
`
`65
`
`Fig. 4. Sampler time-domain response for different values of
`sampler efficiency e and hold efficiency B.
`
`lOOOA> efficiency, e = 1, would require that the sampler on-
`' time be several RC time constants long, but this would mean
`an excessively small input bandwidth, as shown by the GRF
`portion of the sample-and-hold circuit frequency response
`equation in Fig. 3. Most microwave samplers have relatively
`low voltage transfer efficiencies, usually significantly less
`than 10%. With this low sampling efficiency, the resultant
`voltage on the hold capacitor is a weighted combination of
`the input voltage from many samples. Sample-to-sample
`independence is not achieved.
`
`An ideal sample-and-hold circuit also holds its sampled volt(cid:173)
`age indefinitely until either a reset or the next sample occurs.
`The voltage droop from one sample to the next is character(cid:173)
`ized by the hold efficiency B, which can be computed as:
`
`where ts is the sampling period and Rp is the sample-and(cid:173)
`hold circuit's load resistance as defined in Fig. 3. 100% hold
`efficiency means no droop and an infinite load impedance.
`Fig. 4 shows the time-domain re~mlts of sampling a pulse
`waveform with a sample-and-hold circuit that has ideal char(cid:173)
`acteristics, with reduced sampler efficiency, and with re(cid:173)
`duced hold efficiency. Fig. 5 plots the G1F portion of the
`sample-and-hold circuit's frequency response equation for
`sampler efficiencies of 100%, 10%, and 1%, and for hold effi(cid:173)
`ciencies of 900A> and lOOOA>. For low sampler efficiencies like
`those normally encountered in microwave samplers, the
`plots in Fig. 5 look very muc:ti like a single-pole, low-pass
`filter. The equations for GIF do indeed simplify and con(cid:173)
`verge, in this case, to a single-pole filter. The efficiency
`equations become:
`
`E = t 0n/RC
`
`The original model then becomes the very commonly used
`model shown in Fig. 6. The sampler is simply replaced by its
`time averaged impedance Rtsfton·
`
`This characterization of the sampler model points out the
`Ihain difficulties of using a microwave sampler as a sample(cid:173)
`and-hold circuit. The IF output voltage is low-pass filtered
`and represents an av:erage of many samples of the input
`voltage. In addition, if the hold efficiency is not very close to
`1, even the low-frequency gain will vary with the sampling
`
`RPX-Farmwald Ex. 1036, p 3
`
`

`
`RtJton
`
`Fig. 6. Simplified sampler model.
`
`IF and ADC Operation
`Now that the signal has been sampled and the sampler pole
`effect has been canceled, the IF signal can be processed and
`digitized. The IF processing block diagram is ~hown in Fig. 7.
`The ADC used in the HP 70820A is a 10-bit device, operating
`at the same frequency as the input sampler. This 10-bit reso(cid:173)
`lution does not provide enough dynamic range for many of
`the measurements performed by the microwave transition
`analyzer. For example, network analysis measurements can
`be performed over a greater-than-100-dB range and time(cid:173)
`domain waveforms of 1 m V full scale can be captured with(cid:173)
`out requiring trace-to-trace averaging. To achieve this dy(cid:173)
`namic range improvement, step gains are placed in the IF
`signal path. Up to 60 dB of gain in 6-dB steps can be switched
`in, either autoranged or manually controlled by the user.
`This means that even low-level signals can use the full range
`and accuracy of the ADC. To allow gain to be used even in
`the presence of a large de signal, a de offset DAC is added
`ahead of the step gains as shown in Fig. 7. This allows up to
`±420 m V of offset to be applied to the IF signal before the
`step gains. The de offset capability does not affect the al(cid:173)
`lowed input signal range. It must be kept less than 420 m V
`peak to avoid sampler compression.
`
`The total noise present in the IF may mask the input signal
`and limit the amount of step gain that can be used without
`overranging the ADC. This noise is there because the sam(cid:173)
`pler translates the entire 40-GHz bandwidth into the IF fre(cid:173)
`quency range. The programmable-zero amplifier also adds a
`lot of high-frequency amplification to the sampler and the IF
`buffer noise floor. All of this noise needs to be minimized. It
`is also highly desirable to remove any harmonics of the sam(cid:173)
`pling LO signal and signals centered around them. To solve
`these problems, switchable low-pass IF filters are used.
`These include a 10-MHz filter for sampling rates between 14
`
`and 20 MHz and a 7-MHz filter for sampling rates less than
`14 MHz. In addition, a 100-kHz analog noise filter can be
`switched in to provide a greater-than-20-dB reduction in
`total noise. Since this noise filtering is done in real time, it
`provides faster signal-to-noise ratio improvement than the
`digital signal processor-based alternatives.
`
`As described in the article on page 48, the IF signal is a time(cid:173)
`scaled version of the original RF signal when the instrument
`is operating in the standard, repetitive sampling mode.
`Therefore, triggering information can be obtained from the
`IF signal. Since the signal is at a much lower frequency and
`is potentially amplified and filtered, the trigger circuitry is
`cheaper to implement and more accurate than a trigger cir(cid:173)
`cuit operating directly on the.microwave signals. This allows
`the microwave transition analyzer to trigger internally on
`very low-level periodic signals anywhere in its microwave
`frequency range.
`
`Once the IF signal has been filtered, offset, and amplified, it
`is ready to be digitized. The ADC is a commercially avail(cid:173)
`able, two-pass, 10-bit ADC and the required external sample(cid:173)
`and-hold circuit is implemented with a discrete design. The
`sample-and-hold circuit and ADC are driven at the same
`frequency· as the microwave input sampler. The digitized
`signal is stored into the 256K-sample ADC memory buffer
`for further digital signal processing.
`
`IF Corrections
`Fig. 8 shows a representation of the spectrum of the analog
`IF signal for a sample rate of f s = lits. The ideal sampling
`operation creates a spectrum that is replicated every fs so
`the spectral component at f2 = fs - f 1 is the complex conju(cid:173)
`gate of the ideal spectral component at f 1. The IF proces(cid:173)
`sing, including the hold operation of the microwave input
`sampler and the low-pass filters, provides a different
`amount of attenuation and phase shift at the IF frequency f2
`than at frequency f1. This is signified by the G(f) transfer
`function in Fig. 8. When the ADC sample-and-hold circuit
`resamples the IF signal, the spectral component at f 2 will be
`aliased or folded onto the same frequency as f1. It is not pos(cid:173)
`sible to build a perfect anti-aliasing. filter that will totally
`eliminate f 2, even at a fixed sample frequency of 20 MHz,
`and in this app1ication, where the sample· rate is continuously
`variable between 10 and 20 MHz, there will be significant
`
`Fig. 7. Microwave transition analyzn IF block diagram.
`
`66 October 1992 Hewlett-Packard Journal
`
`RPX-Farmwald Ex. 1036, p 4
`
`

`
`Sampled
`Spectrum
`and
`IF Shape
`
`v,
`
`f,
`
`Because of Front-End Sampling Operation,
`V2(f2) = V1 *(f1)
`
`Because of IF Shape and LO Delays,
`V1F2lf2) = V2(f2) G(f2)
`V1F1(f1) = V1(f1) G(f1)
`
`Because of Folding in ADC Sample-and-Hold Circuit,
`VAoclf1) = V1F1lf1)+V1F2*(f2)
`
`VAoclf1l = V11f1l [G(f1l+G*lfs -f,)]
`
`Folded IF Response
`
`Fig. 8. Spectrum folding in the microwave transition analyzer:
`
`aliasing. However, since the filtered IF signal was originally
`a sampled signal, the relationship between the original
`aliased spectrum and the unaliased spectrum is known:
`
`V2 =Vi*·
`
`Therefore, the original spectrum can be computed if the
`folded IF response (G(f 1) + G*(fs - f i)) can be determined.
`The folded frequency response varies with f5, and f5 can be
`any value between 10 and 20 MHz. Therefore, the IF cannot
`realistically be calibrated just by measuring the folded IF
`response, since there are an almost unlimited number of
`different responses possible. Instead, the unfolded frequen(cid:173)
`cy response G(f) must be determined and then the folded
`response can be computed based on the present value of f5•
`Determining the folded IF response is the major requirement
`for the digital signal processor-based IF correctio~s in the
`microwave transition analyzer.
`
`Many things contribute to the overall IF frequency response.
`In addition to the flatness of the IF buffer amplifier, the
`programmable-zero amplifier, and any nonideal cancellation
`of the sampler pole, all possible combinations of analog fil(cid:173)
`ters and step gains must be characterized. For example, the
`relatively high-order filters may have an amplitude response
`flatness of ±2 dB and some very significant group delay vari(cid:173)
`ation which creates considerable ringing in their step re(cid:173)
`sponse. To measure these, the microwave transition analyz(cid:173)
`er generates a calibration signal. The calibration signal is a
`precisely known square wave that is connected by the user
`to the input port. The frequency and amplitude of the cal(cid:173)
`ibration signal are adjusted and varied as required during
`the IF calibration process. This calibration signal is only
`used for IF calibration and verification. The rise and fall
`time requirements on the calibration signal are governed by
`the requirement that it settle in less than 50 ns, so it is not
`useful for verifying or calibrating the RF frequency response
`of the input.
`
`The IF frequency response must be measured in an alias(cid:173)
`free fashion and at frequencies higher than 10 MHz. This
`cannot be done with just a 20-MHz maximum sample rate.
`The exclusive-OR control shown in Fig. 7, which inverts and
`
`delays the ADC clock, helps solve this problem. By first
`measuring the calibration signal with a normal 20-MHz clock,
`and then remeasuring the same signal with the inverted
`clock, which delays the ADC sample by 25 ns, an effective
`40-MHz sample rate is achieved after the two measurements
`are interleaved. In this way, the frequency responses, both
`magnitude and phase, of the IF path, the step gains, and the
`switched filters are all determined. In some cases the mea(cid:173)
`sured data is used directly in the correction process. In other
`cases, such as for the step gains, better results are achieved
`by fitting the measured data to a model and then computing
`the extrapolated frequency response from the model.
`
`The other critical parameter that must be included in the IF
`frequency response is the delay between the microwave
`input sampler and the ADC sample-and-hold circuit. This
`must include both the IF signal delay and the delay in the LO
`clock paths. Since this delay is not constant with sample
`frequency, it must be characterized as a function of the sam(cid:173)
`ple frequency. A significant portion of the IF calibration time
`is spent doing this characterization. This involves measuring
`the group delay of the harmonics of the calibration signal at
`different sample frequencies.
`
`Once the unfolded frequency response and the delay have
`been measured, the folded frequency response can be com(cid:173)
`puted for a given sample frequency. However, since the V 1
`and V 2 spectral components can have very similar ampli(cid:173)
`tudes, it may turn out that the folded frequency response has
`a very deep null in it, depending on the phase relationships.
`An excessively deep null cannot be properly corrected, for
`both noise and stability reasons. When this occurs, the firm(cid:173)
`ware in the microwave transition analyzer must change the
`delay relationship between the IF signal and the ADC clock.
`This can be done with either the ADC clock invert/delay
`control or by using a different 20-MHz analog filter in the
`signal path. The firmware determines which of the possible
`combinations results in the best possible folded frequency
`response.
`
`Once the IF calibration process has been completed, the
`data is stored in battery backed-up RAM. Whenever the sam(cid:173)
`ple frequency or IF gain is changed, the microwave transi(cid:173)
`tion analyzer firmware recomputes the folded frequency
`response of the IF. This folded response is then inverted and
`applied to the digitized input data using either an FFr (fast
`Fourier transform) operation or a 64-point FIR (finite impulse
`response) digital filtering operation, depending on the mea(cid:173)
`surement mode. The result is that the IF looks as if it has a
`flat response all the way to the Nyquist frequency (fsf2).
`Therefore; the microwave sampler appears to have the ideal
`impulse and step response expected of a true sample-and(cid:173)
`hold circuit.
`
`Sample Rate Synthesizer
`The requirements on the sample-rate synthesizer in the
`microwave transition analyzer are quite stringent. Not only
`must it have a frequency resolution less than 0.001 Hz over a
`10-to-20-MHz frequency range, but it must also be able to
`phase-lock to a common 10-MHz reference and be capable
`of shifting the phase of the synthesized output with less than
`0.001-degree resolution. Fortunately, this type of source,
`using fractional-N synthesis techniques, 2 had been used in
`earlier HP instruments and could be efficiently leveraged.
`
`October 1992 Hewlett-Packard Journal
`
`67
`
`RPX-Farmwald Ex. 1036, p 5
`
`

`
`10to20MHz
`Output
`
`10-MHz
`Reference
`
`Fractional-N Assembly
`
`Fig. 9. Block diagram of the
`10-to-20-MHz sample rate synthe(cid:173)
`sizer. API stands for analog phase
`interpolation.
`
`The most stringent requirement for the source was its jitter,
`or equivalent phase noise, but the available implementations
`had inadequate performance. Both the close-in and the
`broadband phase noise of the synthesizer are important. For
`example, just based on the maximum slope of a full-scale
`40-GHz sine wave, jitter of 7 femtoseconds on the sampler
`LO signal generates additional noise greater than one least(cid:173)
`significant bit of the ADC. Since the fundamental of the RF
`waveforms can be mixed to as low as 100 Hz in the IF, mini(cid:173)
`mizing the close-in noise and spurious components of the
`sample-rate synthesizer is critical to avoiding low-frequency
`perturbations and distortion of the digitized signal.
`
`To improve the basic performance of the available
`fractional-N synthesizers while still leveraging much of the
`previous engineering effort and available integrated circuits,
`a translate loop was added to the normal synthesizer block
`diagram. As seen in Fig. 9, instead of having the loop oscilla(cid:173)
`tor operate directly over the normal 30-to-50-MHz band, a
`420-to-440-MHz oscillator is mixed with a 390-MHz reference
`oscillator. The mixer output, 30 to 50 MHz, is the input to the
`leveraged fractional-N assembly, which does the fractional
`division, phase detection, and interpolated phase correction,
`and generates the tuning voltage to lock the 440-MHz oscilla(cid:173)
`tor. A second output of the 440-MHz oscillator is fed to a
`programmable integer divider to generate the 10-to-20-MHz
`output.
`
`There was no requirement for this synthesizer to sweep con(cid:173)
`tinuously over the 10-to-20-MHz range. This translate-and(cid:173)
`divide-down block diagram allows the performance of the
`overall synthesizer to be improved from the original design
`by a factor equal to the integer divide number, or more than
`26 dB. To improve the broadband phase noise further, a
`200-kHz-wide bandpass filter is switched in just before the
`step recovery diode driver whenever the synthesizer is with(cid:173)
`in the 19.8-to-20-MHz frequency range. In the majority of the
`measurement modes, the synthesizer is set very close to 20
`MH~, so this bandpass filter is normally used. While it was
`not possible to achieve the 7-fs performance number, this
`
`combination of improvements reduces the jitter contribution
`of the synthesizer to less than 1 ps.
`
`RF Filtering
`Because the microwave transition analyzer digitizes wave(cid:173)
`forms with a continuous and extremely precise time axis, it
`becomes feasible to apply digital filtering functions to these
`waveforms. These filters can be used to simulate the adding
`of a hardware filter to the system, to improve the signal-to(cid:173)
`noise performance, to remove undesired harmonics and
`spurious frequency components, and to compensate for non(cid:173)
`ideal microwave frequency response effects in the RF cir(cid:173)
`cuitry, cabling, probes, and test fixtures, which inevitably
`degrade the system bandwidth. This ability to correct for RF
`frequency response roll-off is also used within the instru(cid:173)
`ment to flatten the frequency response of both the samplers
`and the internal RF cabling to 40 GHz.
`
`Two filters can be defined by the user, one for each of the
`two input channels. These filters are specified by defining.
`the magnitude and phase response at up to 128 arbitrarily
`spaced frequency points. The type of interpolation to be
`used between these frequencies can be specified as flat,
`linear, or logarithmic. These user-defined filters are com(cid:173)
`bined with the instrument's own RF correction data to gen(cid:173)
`erate the composite filter function that is applied to the digi:(cid:173)
`tized signal. Regardless of whether the sampler is being
`used for frequency translation or frequency compression or
`a combination of the two, there is a unique mapping be(cid:173)
`tween the input RF frequency and the IF frequency. This ·
`means that the desired RF filtering can indeed be performed
`by scaling and translating the filters' frequency axis, based
`on the current time span and carrier frequency, into the IF
`band and performing the filtering on the digitized IF signal.
`
`There are some modes of sampler operation in which the RF
`waveform is not replicated in the IF, so there is no unique
`RF-to-IF frequency mapping and RF filtering cannot be per(cid:173)
`formed. An example of this mode of operation would be
`when triggering on the-clock frequency while sampling a
`
`68 October 1992 Hewlett-Packard Journal
`
`RPX-Farmwald Ex. 1036, p 6
`
`

`
`was taken and stored to the user correction filter as the
`cable fixture's frequency response. This is shown on the
`bottom trace in Fig. 10 out to a frequency of 8 GHz. A test
`pulse of of 800 ps was then used. The upper raw trace shows
`the pulse distortion caused by the cable fixture. After user
`corrections were turned on, the corrected trace was gener(cid:173)
`ated, which lies almost directly on the ideal trace. The ideal
`trace was established by measuring the pulse directly out of
`the pulse generator before it was connected to the cable
`fixture. The time-domain traces are showing a half cycle of a
`200-MHz pulse train.
`
`There are some limitations on the ability of the microwave
`transition analyzer to apply RF filtering and correction to
`time-domain waveforms. First, the IF waveform must be a
`valid representation of the RF waveform. If there are non(cid:173)
`harmonically related, spurious, or random signals present,
`they will be mixed into the IF but will not appear at the cor(cid:173)
`rect frequencies, so incorrect filter values will be applied to
`them. Second, the signal must be sampled with fine enough
`equivalent time resolution to avoid aliasing any significant
`harmonics or sidebands. This is just the Nyquist criterion,
`which says that a signal must be sampled at a rate ·greater
`than twice its single-sided bandwidth. This applies to both
`real-time, single-shot sampling and repetitive, equivalent
`time sampling. Any aliased components will appear at the
`incorrect frequencies and be improperly filtered.
`
`Third, because limited time records are captured and pro(cid:173)
`cessed with the FFT, totally arbitrary filter shapes cannot, in
`general, be precisely accommodated. For example, a filter
`shape with a 2-µs transient response would r.equire that 2 µs
`of an arbitrary input be digitized to generate even the first
`output point. A desired time resolution of 1 ps would require
`two million data samples and a digital filter with effectively
`two million coefficient taps. There are two methods avail(cid:173)
`able to minimize this limitation. If an integer number of
`cycles of the input are used in the FFT processing, then arbi(cid:173)
`trary filter shapes can be precisely handled. The circular
`convolution performed by the FFT is, in this case, exactly
`equivalent to the desired linear convolution. To make this
`more practical to the user, a cycles mode is available in
`which the time span can be set in terms of cycles of the fun(cid:173)
`damental instead of seconds per division. This automatically
`tracks the fundamental frequency as it is changed. The micro(cid:173)
`wave transition analyzer oversweeps the time-domain span
`up to the next largest power-of-two trace size. For example,
`if a 0.5-cycle time span is specified with a trace point size of
`512, then one full cycle of the waveform is digitized and a
`1024-point FFT is used ..
`
`The second method of minimizing the effect of limited time
`records is to make sure that the filter's transient response is
`shorter than the minimum displayed time span to be used. If
`the waveform used in the FFT does not contain an integer
`number of signal periods, there will potentially be edge ef(cid:173)
`fects because of the combination of the discontinuity at the
`edges of the time record and the filter's transient response.
`Since the instrument oversweeps up to a factor of two, the
`edge effects will not be part of the displayed waveform as
`long as the filter has a transient response shorter than the
`displayed time span.
`
`October 1992 Hewlett-Packard Journal
`
`69
`
`Tr1=Correct
`30 mU/div
`0 U ref
`
`Tr2=1deal
`30 mUldiv
`0 U ref
`
`Tr3=Raw
`15 mU/div
`0 U ref
`
`250 psldiv
`TrY=Ucorr1
`10 dB/div
`0 dB ref
`
`Fig. 10. An example of a measurement with user filter corrections.
`The frequency response of a cable fixture was measured (bottom
`trace), stored, and used to correct a measurement of an 800-ps
`pulse that was made using the fixture. The corrected trace mea(cid:173)
`sured with the fixture is almost identical to the ideal trace mea(cid:173)
`sured without the fixture. Because the ideal and corrected traces
`are almost identical, they are. indistinguishable in this figure .
`
`random data sequence to create an eye diagram. User filter(cid:173)
`ing, including the internal RF corrections to 40 GHz, is not
`valid in this mode so the feature must be turned off. If, how(cid:173)
`ever, the data sequence is actually a pseudorandom data
`sequence and the sample rate of the microwave transition
`analyzer is adjusted to correspond to the pattern repetition
`rate instead of the clock rate, then the RF waveform is repli(cid:173)
`cated in the IF, and RF filtering and corrections can be per(cid:173)
`formed, even while triggering on the clock to make eye
`diagram measurements.
`
`The u