Tracking Technology in Pulse S-Parameter Measurement

     S-parameter testing with a vector network analyzer is usually done by applying continuous wave excitation to the device under test. However, in some cases, pulsed excitation is necessary for S-parameter measurement. For example, when testing the S-parameters of non-thermally coupled devices under test, such as power transistors, the heat accumulated by continuous wave excitation may damage the device under test, while the use of pulsed excitation for measurement can safely characterize the characteristics of such devices. By properly selecting the duty cycle of the pulsed excitation, the average power of the measurement can be kept at a low level to avoid overheating. Another example of the need for pulsed S-parameter measurement is the measurement of devices that usually operate in a pulsed or burst signal state, such as radar systems and many digital modulation communication systems. Today, pulsed S-parameter measurements can be completed using vector network analyzers that can generate pulsed excitation and accurately measure pulsed sinusoidal signals.

　　The spectrum of the pulse signal can be expressed with the help of some mathematical analysis tools. Equation 1 describes the pulse signal in the time domain. The generation process of the pulse signal can be intuitively expressed as follows: First, a rectangular window signal [rect(t)] is established for the pulse width PW pulse signal to be generated;
　　y(t) = (rect pw (t)×x(t))×shah 1(t) (1)

 

　　Figure 1
　　then generates a shah function, which consists of a periodic impulse train with an interval of 1/PRF, where PRF is the repetition frequency of the pulse signal to be generated. The shah function can also be regarded as a number of impulses with an interval equal to the period of the pulse signal. Finally, the window signal is convolved with the shah function to generate a periodic pulse train that is consistent with the desired pulse signal in time.

　　Equation 2 represents the Fourier transform of a pulse signal in the time domain. It shows that the frequency spectrum of a pulse signal is a sinc function with a sampling frequency equal to the pulse repetition frequency (PRF).
　　Y (s) = ( pw · sinc ( pw · s) · X (s)) · ( prf · shah ( prf · s))
　　Y (s) = ( pw · sinc ( pw · s)) · ( prf · shah ( prf · s))
　　Y (s) = DutyCycle · sinc ( pw · s) · shah ( prf · s) (2)
　　Figure 1a shows the spectrum of a pulse signal with a PRF of 1.69 kHz and a pulse width of 7 µs. Figure 1b shows the same pulse spectrum zoomed in on the fundamental frequency, the frequency of the pulsed signal (the center of Figure 1a). Note that the spectrum contains components that are nPRF away from the fundamental frequency. The fundamental frequency contains the information needed for measurement; the components separated by PRF are generated during the pulse processing of the fundamental frequency. It is worth noting that the amplitude of the spectral components close to the fundamental frequency is relatively large.

 
　　Fig.1aFig.1b
 
　　​

      These figures show the pulse spectrum of a signal with a PRF of 1.69 kHz and a pulse width of 7 µs (a), and the same pulse spectrum zoomed in to the fundamental frequency (center of the figure) (b).

　　Agilent PNA-X series vector network analyzers can provide pulse excitation and accurately test pulse response. This highly integrated S-parameter measurement system (Figure 2a) contains complex signal generation and distribution components (Figure 2b), which enables it to perform both continuous wave excitation response tests and pulse signal excitation response tests. The internal signal source can modulate the internal test signal generator to generate pulse excitation from 10 MHz to 26.5 GHz. This internal signal source of the vector network analyzer can generate pulse signals with a minimum pulse width of only 33 ns (typical values ​​are even narrower).

　　The timing signal for pulse measurement is generated by a pulse generator inside the PNA-X. This pulse generator has four main output channels, each with independent pulse delay and width control. These output channels can directly drive the modulator and data acquisition circuit inside the PNA-X through the internal path of the PNA-X, or they can be output from the rear panel of the PNA-X to the outside of the PNA-X to drive other peripheral test equipment. The timing of the pulse generator is based on a 60 MHz clock signal, generating a timing signal with a resolution of 16.7 ns. Since these pulse generators are independent of

　　Each measurement channel can set the pulse generator independently, so that various test items can be measured and displayed at the same time, such as the measurement results of pulse envelope, pulse point and gain compression can be displayed on one display screen at the same time. Whether it is continuous wave measurement or pulse signal measurement, the receiver of PNA-X is designed for optimal sensitivity.
 

　　Figure 2a
 

　　Figure 2b

The Agilent PNA-X vector network analyzer (VNA) can perform pulsed S-parameter measurements using both wideband and narrowband measurement modes (b) with the help of internal complex signal routing (b).

　　The PNA-X microwave vector network analyzer can perform pulse measurements in both broadband and narrowband modes, each of which has its own advantages and trade-offs. Agilent PNA-X, a series of modern vector network analyzers, has both detection modes, so instrument users can flexibly customize measurement plans when testing the characteristics of test devices.

　　Wideband detection is used when the majority of the pulse spectrum falls within the VNA receiver IF bandwidth. Wideband detection can be implemented using either analog circuit technology or digital signal processing. With wideband detection, the network analyzer receiver detector is synchronized with the pulse stream and data is acquired only when the pulse is present (the pulse is in the "ON" state). Because this method uses a pulse trigger signal synchronized to the PRF to trigger the VNA, this mode is often referred to as synchronous acquisition mode (Figure 3). The time resolution of this mode is a function of the receiver detection bandwidth (IFBW). A good reference standard for determining the appropriate time resolution is to use the reciprocal of the receiver IF bandwidth, i.e., 1/IFBW, as the time resolution value.

　　Figure 3
　　For wideband detection in a VNA, the detector is synchronized with the pulse stream being measured and data is acquired only when the pulse is in the “on” state. Because the pulse triggering in the VNA is synchronized with the PRF, this measurement method is often referred to as synchronized acquisition mode.

　　The advantage of the wideband test mode is that there is almost no loss in dynamic range when testing pulse signals with a large duty cycle (with a relatively stable signal-to-noise ratio and duty cycle relationship). The disadvantage is that the minimum pulse width that can be measured is limited. As the pulse width of the signal becomes narrower and narrower, the signal spectrum energy will be distributed in a wider bandwidth. When enough pulse energy falls outside the intermediate frequency bandwidth of the receiver, the receiver cannot properly detect the pulse. From a time domain point of view, when the width of the pulse is less than the rise time of the receiver, the receiver cannot detect the pulse. To measure narrower pulses, (if you continue to use the wideband mode for testing) you must use a wider detection bandwidth. As the receiver bandwidth increases, more noise will enter the receiver, thus reducing the dynamic range of the measurement.

　　The PNA-X microwave vector network analyzer has a detection (IFBW) bandwidth of up to 5 MHz in broadband test mode, with a time resolution of approximately 250 ns (the minimum pulse width that can be accurately measured). Configuring the PNA-X in broadband mode is very simple. The pulse generator can be configured not only to trigger the internal signal source modulator, but also to trigger the measurement internally, so that data acquisition is synchronized with the incoming RF pulse (no external trigger cable required). In this case, the PNA-X can be configured to measure the point-in-pulse, the pulse profile, and the relationship between pulses (Pulse-to-Pulse) on a single display interface.

　　In narrowband detection mode, the pulse width is usually much smaller than the minimum time required to digitize and collect data for a discrete data point (Figure 4). Using narrowband test technology, all spectral components in the pulse spectrum are filtered out except for the center frequency component representing the RF carrier frequency. After filtering, the pulse RF signal becomes a sinusoidal (i.e., continuous wave) signal. When the vector network analyzer operates in narrowband pulse measurement mode, each data sampling point is not synchronized with the input pulse, so there is no need for a synchronous measurement trigger signal, so narrowband detection technology is also called asynchronous acquisition mode. Generally speaking, in narrowband test mode applications, because the PRF of the measured pulse signal is higher than the intermediate frequency bandwidth of the receiver, this method is also called "high PRF" mode.

　　Figure 4

　　In narrowband detection mode, the pulse width is usually much smaller than the minimum time required for digitizing and acquiring a discrete data.
　　Agilent has developed a better narrowband test technology on PNA-X. This new narrowband test technology can make the IFBW of the test receiver wider than the IFBW commonly used in narrowband test mode in the past. This unique method is called "zero-point spectrum technology" (Figure 5). This very efficient detection mode method generates a "matched" digital filter based on the PRF of the pulse signal. This technology allows users to trade a little loss in dynamic range for faster test speeds, which can always achieve faster test speeds compared to pulse measurements performed by traditional filtering methods.

 
　　Figure 5

　　Partial implementation of narrowband detection over wider IF bandwidths in the PNA-X VNA requires the use of matched digital filters based on the PRF of the pulse signal being measured.

　　Generally speaking, since the narrowband test method filters out all other pulse spectrum components except the center spectrum, it is significantly less restricted in terms of the narrowest pulse width that can be tested. The disadvantage is that the dynamic range of the measurement is affected by the duty cycle. When the duty cycle is small (the interval between pulses is long), the decrease in the average power of the pulse will cause a decrease in the signal-to-noise ratio (SNR), which will lead to a decrease in the measurement dynamic range.

　　It decreases with the decrease of duty cycle. We call this phenomenon "pulse desensitization". In Agilent's previous generation of vector network analyzers with pulse test capability (PNA series products), the amount of reduction in test dynamic range due to the decrease of duty cycle can be calculated using the 20log (duty cycle) relationship. PNA-X has greatly improved the pulse desensitization of the receiver by adopting a new advanced pulse detection method.

　　PNA-X has greatly improved the above limitations by adopting new hardware and software techniques and algorithms, significantly reducing the pulse desensitization effect related to 20log(duty cycle). The two major improvements are the use of enhanced hardware gating and software gating. In order to improve the time resolution of PNA-X, a gating switch is added to the IF path of PNA-X (Figure 6). The timing signal of the gating switch comes from one of the several output channels of the internal pulse generator of PNA-X (Figure 2b), which sets the pulse period, pulse width and delay. The gating width of the gating switch provides time resolution for fixed-point measurements in the pulse and pulse envelope measurements.

　　Figure 6

　　The PNA-X minimizes pulse desensitization through a variety of new techniques, including the use of gating switches in the IF path to improve time resolution.

　　Since the noise figure of the entire IF path is often determined by the first few stages upstream of the receiver, the signal-to-noise ratio can be improved by providing as much gain as possible to the signals (and noise) from the upstream receiver before they reach the IF gate (the signal size should be chosen so that the gate does not operate in the compression region, so that the energy of the peak pulse envelope can pass through the gate relatively unaffected), and then using the gate switch for time discrimination (time resolution). Since the duty cycle is related to the repetition rate and gate width of the gate switch (because the timing signal of the gate switch comes from an output channel of the pulse generator that determines the pulse period, pulse width and pulse delay, as shown in Figure 2b), when the noise power (in dB) is reduced according to the relationship of 10log(duty cycle), the power (in dB) of the center frequency component of the pulse spectrum will be reduced according to the relationship of 20log(duty cycle) (Figure 6). The overall result is that the measurement dynamic range degrades at a rate closer to 10log(duty cycle) rather than 20log(duty cycle) as in the PNA-X's previous generation of vector network analyzers.

　　The crystal filter in Figure 6 is used to remove unwanted pulse spectrum and additive noise before the pulse reaches the downstream amplifier and digitizer. Note that removing these pulse spectrum components reduces the peak envelope response, thereby preventing compression in downstream components and reducing system noise. In previous hardware gating implementations, the noise figure of the circuit components after the gating switch was not much better than the noise figure of the circuit components before the gating switch, so there was no reduction in digitized noise power after gating. This process does not actually gate the noise power (noise power does not change with gating), so the measurement dynamic range changes by 20log(duty cycle).

　　After the ADC, the digitized data is filtered using a spectrum-nulling matched filter to remove all residual pulse spectrum except the desired RF carrier.

　　Narrowband detection mode is an asynchronous pulse measurement method where the digitizer continuously measures the signal while the analyzer processes all digitized information. This means that data can still be sampled and processed even when the gate is off (Figure 7). Any residual amount of isolation and noise with the IF gate off is undesirable because the only signal we are interested in is the signal we see when the gate is on. Ideally, a perfect gate would have no signal or noise in the off state to avoid converting too much noise into the digital signal, which would increase measurement noise and reduce the accuracy of the measurement result.

 
　　Figure 7

　　Because the digitizing processor is always sampling in narrowband detection mode, it can capture both the signal and the noise from the gate switch in the off state.

      One way to remove these undesirable residuals that exist when the gate switch is in the off state is to use software gating (Figure 8). The benefit of integrating the pulse generator with the vector network analyzer is that the timing of the pulse generator is precisely known, and therefore the timing of the gate switch turning on and off is also precisely known. Once the data has been digitized, time stamps can effectively be placed on the digital data corresponding to when the gate switch was turned on and off. This way, it is known which portion of the digital data corresponds to the on state of the gate switch and which portion of the digital data corresponds to the off state of the gate switch. Since only the residual noise in the off state of the gate switch will degrade the measurement accuracy, this digital data can be deliberately set to zero, making it an ideal component with neither noise nor signal. In this way, the measurement sensitivity is greatly improved because the noise component of the SNR has been significantly reduced.

　　Figure 8

　　Software gating can be used to remove unwanted signals and noise remaining in the off state of the gating switch.

　　The implementation of enhanced hardware and software gating methods significantly improves test sensitivity compared to previous vector network analyzer narrowband detection techniques. Figure 9 shows the improvement in dynamic range using different pulse detection techniques. This is a very difficult measurement example with very low duty cycle (0.001%) and very narrow pulse width. The PNA-X hardware and software improvements complement each other perfectly, as the hardware gating reduces noise on noisy circuits in the link upstream of the receiver before the receiver is gated, while the software gating algorithm further reduces noise by eliminating noise in the off state of the gate switch. These technical advances have led to a significant improvement in pulse test sensitivity, which has greatly improved the accuracy of test results.

 
　　Figure 9

　　In this example, different pulse detection techniques provide different levels of dynamic range performance for low (0.001%) duty cycle pulse signals.

　　The integration of hardware and the improvement of measurement algorithms have greatly improved the sensitivity and accuracy of pulse S parameter measurements using modern vector network analyzers - Agilent PNA-X series. Wideband and narrowband detection modes provide flexible measurement solutions for accurately measuring the pulse S parameters of the device under test. Compared with previous narrowband detection technology, these advanced features can greatly increase the dynamic range. PNA-X series network analyzers need to be configured with options 021, 022, 025 and H08 to perform pulse S parameter measurements.