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 [rect(t)] 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 µs. 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.

Continued on page 2