Scattering (S) parameter measurements with a vector network analyzer (VNA) are usually performed with a continuous-wave (CW) stimulus applied to the device under test (DUT). In some cases, however, it may be necessary to use a pulsed stimulus for the S-parameter measurements. For example, a DUT that is not thermally coupled (such as a power transistor) might be damaged by the heat buildup of CW measurements, but safely characterized by pulsed measurements. By properly selecting the duty cycle of the pulsed stimulus, the average power of these measurements can be kept low to avoid overheating. Another example is the measurement of a DUT that might normally operate with pulsed or burst signals, as found in radar systems and many digital-modulation communications systems. Pulsed S-parameter measurements rely on a VNA that can generate as well as accurately measure pulsed sinusoidal signals.
The spectrum of a pulsed signal can be visualized through the aid of some mathematical analysis. Equation 1 describes a pulsed signal in the time domain. A visual representation of a pulsed signal is generated by first creating a rectangular windowed version of a signal with pulse width PW.
A shah function is then realized. This function consists of a periodic train of impulses spaced 1/PRF apart where PRF is the pulse repetition frequency. This can also be viewed as impulses with spacing equal to the pulse period. The windowed version of the signal is then convolved with the shah function to generate a periodic pulse train in time corresponding to the pulsed signal.
Equation 2 presents the Fourier transform of a pulsed signal in the time domain. It illustrates that the frequency-domain spectrum of the pulsed signal is a sampled sinc function with sample points (signal present) equal to the PRF.
Figure 1a shows an example pulsed spectrum for a signal with a PRF of 1.69 kHz and pulse width of 7 s. Figure 1b shows the same pulsed spectrum zoomed in on the fundamental frequency that is pulsed (center of plot). Notice that the spectrum has components that are nPRF away from the fundamental tone. The fundamental tone contains the measurement information. The PRF tones are artifacts of pulsing the fundamental tone. It is also worth noting that the magnitudes of the spectral components close to the fundamental tone are relatively large.
Agilent PNA-X Series VNAs from Agilent Technologies (www.agilent.com) are capable of supplying a pulsed stimulus and accurately measuring pulsed responses. The highly integrated S-parameter measurement system (Fig. 2a) contains sophisticated internal signal routing (Fig. 2b) that enables it to generate and analyze both CW and pulsed stimulus responses. Internal test-signal generators are modulated by internal sources to produce pulsed stimuli from 10 MHz to 26.5 GHz.
The VNA's internal sources can generate a minimum pulse width of 33 ns (typically even narrower than this).
The pulse-measurement timing is generated by using an integrated pulse generator, which has four main output channels, each with independent delay and width. The output channels can be routed internally inside the PNA-X to drive the modulators and acquisition circuitry, and/or externally to drive external peripheral devices. The timing of the pulse generators is based on a 60-MHz clock, resulting in 16.7 ns timing resolution. Since these pulse generators are independent of the measurement channels, each measurement channel can have independent pulse generator setting. This allows the simultaneous measurement and display of a variety of measurements, including pulse-profiling, point-in-pulse, and gain compression, on a single display. The PNA-X receivers are designed for optimum sensitivity with both CW and pulsed signals.
The PNA-X VNA can make pulse measurements in wideband and narrowband modes. The two modes have benefits and trade-offs. Modern VNAs such as the PNA-X include both detection modes so that operators have the flexibility to tailor their measurements to the characteristics of the DUT.
Wideband detection is suitable for cases when the majority of the pulsed RF spectrum falls within the bandwidth of the VNA's receiver. Wideband detection can be performed with analog circuitry or digital-signal-processing (DSP) techniques. For wideband detection, the VNA's receiver detectors are synchronized with the pulse stream, with data acquisition occurring only when the pulse is in the "on" state. Because this approach involves a pulse trigger synchronized to the PRF to trigger the analyzer, it is often called synchronous acquisition mode (Fig. 3). The time resolution of this mode is a function of the receiver's detection bandwidth. A good figure of merit for determining the approximate time resolution is to use the inverse of the bandwidth, or 1/BW.
The advantage of the wideband mode is that there is no loss in dynamic range for low-duty-cycle pulses, with a relatively constant signal-to-noise ratio (SNR) versus duty cycle. The disadvantage is that there is a lower limit on measurable pulse widths. As a signal's pulse width becomes more narrow, the spectral energy is spread over a wider bandwidth. When enough of the pulse's energy falls outside of the receiver's bandwidth, the receiver can no longer properly detect the pulse. In the time domain, a receiver can no longer detect a pulse that is shorter than the rise time of the receiver. To measure shorter pulses, a wider detection bandwidth must be used. As the bandwidth of the receiver increases, the amount of noise also increases, decreasing the dynamic range of the measurements.
The PNA-X VNA can provide wideband mode detection at detection bandwidths as wide as 5 MHz; this provides about 250 ns time resolution (the minimum pulse width that can be measured accurately). Configuring the PNA-X in wideband mode is simple. The pulse generator can be configured to not only trigger the internal source modulator but also internally trigger the measurements so that data acquisition is synchronous with the incoming RF pulses (no external triggering cables are required). The PNA-X can then be configured to make point-in-pulse, pulse-profiling, or pulse-to-pulse measurements all on one display.
In narrowband detection mode, the pulse width is usually much less than the minimum time required to digitize and acquire one discrete data point (Fig. 4). With this technique, all of the pulse spectrum is removed by filtering except the central frequency component, which represents the frequency of the RF carrier. After filtering, the pulsed RF signal appears as a sinusoid or CW signal. With narrowband detection, analyzer samples are not synchronized with the incoming pulses (therefore no synchronized measurement trigger is required), so the technique is also known as asynchronous acquisition mode. This approach is also called the "high PRF" mode because the PRF is usually high compared to the receiver's IF bandwidth.
Agilent has developed a novel way of achieving narrowband detection based on wider IF bandwidths than normally used in narrowband mode. This unique approach is called "spectral-nulling" (Fig. 5). In this efficient detection mode method, a "matched" digital filter is generated based on the PRF of the pulse signal. This technique lets the user trade dynamic range for speed, almost always yielding more measurement speed than pulsed measurements performed by conventional filtering.
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The advantage of narrowband detection is the lack of a narrow pulse-width limit, because of the filtering of the spectral components. The disadvantage is that the measurement dynamic range is a function of duty cycle. With smaller duty cycles (longer times between pulses), the average power decreases, resulting in a lower SNR. This results in a decrease in measurement dynamic range with decrease in duty cycle. The effect is known as "pulse desensitization." In previous generations of pulsed VNAs, the degradation in dynamic range (in dB) can be expressed as 20log(duty cycle). The PNAX has substantially improved the receiver pulse desensitization by incorporating new advanced pulse detection schemes.
The PNA-X has greatly improved this limitation with new hardware and software techniques/algorithms, which substantially reduces the pulse desensitization of 20log(duty cycle). Two main advancements are enhanced hardware gating and software gating. For improved time resolution in the PNA-X, a gate switch is placed in the IF path (Fig. 6). The gate switch receives timing from one of the pulse-generator output channels which sets the pulse period, width, and delay. The gate switch width provides the resolution in time for point-in-pulse and pulse profile measurements.
The noise figure of the IF path is often set by the upstream receiver stages. The SNR can be improved by providing as much gain as possible to the signal (and noise) from the upstream receiver path before the IF gate. Levels are set such that the gate switch does not compress and the peak-pulse-envelope energy passes relatively unchanged. The gate switch is then used for time discrimination (time resolution). As the duty cycle changes by the gate switch repetition rate and width, the noise power (in dB) decreases by 10log(duty cycle) and the center frequency component in the pulse spectrum decreases by 20log(duty cycle). The overall result is a dynamic range reduction approaching 10log(duty cycle) instead of 20log(duty cycle) as in previous VNA implementations.
The crystal filter is used to remove undesirable pulse spectrum and additional noise before reaching the downstream amplifiers and digitizers. Note that removing these pulse-spectrum components reduces the peak envelope response, thus preventing downstream compression, as well as reducing the system noise. In previous implementations of hardware gating the noise figure after the gate switch was not a lot better than that before the gate switch so gating the noise did not result in the digitized noise power going down. This resulted in no noise power gating (noise power did not change with gating) leaving the dynamic range changing as a function of 20log (duty cycle). The Spectral nulling matched filter is then applied to the digital data to remove all residual pulse spectrum except the RF carrier of interest.
The narrowband detection mode is an asynchronous pulse measurement where the digitizers are measuring signals continuously with the analyzer processing all of the digitized information. This means that even though the gate switch is off, the data is still being sampled and processed (Fig. 7). Any residual isolation and noise in the off state of the IF gate switch is undesirable since it is what occurs when the gate switch is open that is really of interest. In the ideal case, a perfect gate switch would have no signals or noise in the off state to avoid digitizing excess noise that would otherwise increase measurement noise and degrade the accuracy of the measurement results.
One way of removing the undesirable residuals in the gate switch off state is by using software gating (Fig. 8). One of the advantages of integrating the pulse generator within the VNA is that the precise pulse-generator timing is known and therefore the timing of the gate switch on and off times is also known accurately. Once the data has been digitized, a timing stamp is effectively placed on the digital data that corresponds to when the gate switch was turned on and when it was turned off. This makes it possible to know which elements of digital data correspond to the on state and which elements correspond to the off state of the gate switch. Since the residuals in the off state of the gate only degrade the measurement accuracy, this digital data is set to zero making it a perfect noise-and-signal-free element. This substantially increases the measurement sensitivity since the noise component of the SNR has been decreased dramatically.
The implementation of enhanced hardware and software gating has greatly improved the sensitivity over previous narrowband detection techniques VNA modes. Figure 9 illustrates the dynamic-range improvements using the different pulse detection techniques. This is a challenging measurement case since the duty cycle is very low (0.001 percent) and the pulse width is very narrow. The hardware and software improvements nicely complement themselves, since the hardware gating reduces noise up to the point of excess noise in the upstream receiver chain before the receiver gate and software gating algorithms further reduce the noise by eliminating noise in the off states of the gate switch. The enhancements result in a substantial improvement in pulse sensitivity and therefore measurement accuracy.
Advances in hardware integration and measurement algorithms has greatly increased the sensitivity and therefore the accuracy of pulsed S-parameters using modern VNAs like the Agilent PNA-X Series. Wideband and narrowband detection modes provide flexible measurement scenarios for accurately measuring the pulsed S-parameters of a DUT. These advances yield a significant increase in dynamic range over previous narrowband detection techniques. The PNA-X Series of network analyzers should be configured with Option 021, 022, 025, and H08 to make pulsed S-parameter measurements. For more information on these pulsed measurement configurations, follow the website link to www.agilent.com/find/pna-x.
For Further Reading
Loren Betts, "Make Accurate Pulsed S-Parameter Measurements," Microwaves & RF, Vol. 42, No. 11, November 2003, p. 72.
Agilent Technologies, "PNA/PNA-X Series Microwave Network Analyzers," Agilent Technologies Configuration Guide 5988-7989EN, www.agilent.com.
Agilent Technologies, "Pulsed-RF S-Parameter Measurements Using Wideband and Narrowband Detection," Agilent Technologies Application Note 5989-4839EN, www.agilent.com.
Agilent Technologies, "Pulsed Measurements using the Microwave PNA Series Network Analyzer," Agilent Technologies White Paper 5988-9480EN, www.agilent.com.
Agilent Technologies, "Triggering the PNA Series Network Analyzer for Antenna Measurements," Agilent Technologies White Paper 5988-9518EN, www.agilent.com.
Agilent Technologies, "Pulsed Measurements with the Agilent 8720ES and 8753ES Network Analyzers," Agilent Technologies Product Note, May 2000, www.agilent.com.
Agilent Technologies, "Using a Network Analyzer to Characterize High-Power Components," Agilent Technologies Application Note AN 1287-6, March 2003, www.agilent.com.
J. Barr, R. Grimmet, and R. McAleenan, "Pulsed-RF Measurements and the HP 8510B Network Analyzer," HP RF & Microwave Measurement Symposium and Exhibition, August 1988.
Hewlett Packard, "85108A Pulsed Network Analyzer System," Hewlett Packard System Manual, March 1995, www.agilent.com.
Hewlett Packard, "HP 8510B Pulsed-RF Network Analyzer," HP Users Guide, March 1995, www.agilent.com.
J. Scott, M. Sayed, P. Schmitz, and A. Parker, "Pulsed-bias / Pulsed-RF Device Measurement System Requirements," 24th European Microwave Conference, pp. 951-961, Cannes France, September 5-8, 1994.
J. Swanstrom, R. Shoulders, "Pulsed Antenna Measurements with the 8530A Microwave Receiver," Hewlett-Packard, AMTA conference.
P. Schmitz, M. Sayed, "Techniques for Measuring RF and MW Devices in a Pulsed Environment," Hewlett-Packard Co., February 1993.
B. Taylor, M. Sayed, K. Kerwin, "A Pulse Bias / RF Environment for Device Characterization," 42nd Automatic RF Techniques Group (ARFTG) Conference, San Jose, CA, December 1993.
Hewlett-Packard Co., "Pulsed-RF Network Analysis using the 8510B," HP Product Note 8510-9, Jan 1988 Hewlett-Packard Co., "Spectrum Analysis - Pulsed-RF," HP Application Note 150-2.
D.C. Nichols, "Capture and Analysis of Individual Radar Pulses Using a High-Speed, High-Resolution Digitizer," HP RF & Microwave Measurement Symposium, September 1987.