Measure Group Delay Without Direct LO Access

Group delay that is well controlled in frequency-conversion components, such as mixers, is essential for many high-speed, highfrequency systems. It is critical for achieving low bit-error-rate (BER) performance in wireless and satellite communications receivers and for high target resolution in phased-array radar systems. The typical approach for measuring group delay requires access to the converter's local oscillator (LO) signal. However, the LO is often inaccessible for measurement purposes. Fortunately, a new group-delay measurement technique from Rohde & Schwarz (Columbia, MD) for the R&S ZVA series vector network analyzers (VNAs) makes direct LO access unnecessary and allows the group delay of mixers and frequency converters to be measured with high accuracy.

The R&S ZVA series VNAs (Fig. 1) include instruments with two or four test ports, covering frequency ranges of 300 kHz to 8, 24, 40, 50, and 67 GHz. The VNAs provide intermediate- frequency (IF) bandwidths to 15 MHz (and 30 MHz for pulse profile measurements), and can perform measurements at speeds to 2 microseconds per point when using a 5-MHz IF bandwidth. The VNAs are available with a second internal test source to 50 GHz for two-tone measurements on amplifiers and frequency converters and offer dynamic range of typically better than 145 dB.

The Embedded LO Measurements (R&S ZVA-K9) and Frequency Converter Application (R&S ZVA-K4) options for the R&S ZVA series instruments stimulate a device under test (DUT) with a two-tone signal and measure the phase difference between the two signals at the input and output to obtain the device's phase change. The technique can be used when evaluating devices with single as well as with multiple mixing stages. The key ingredient in this technique is the VNA's ability to measure the phase differences between the two signals at the input and the output of the DUT. These phase differences can be used to calculate the absolute group delay and the relative phase of the conversion loss. The measurement accuracy does not depend on the embedded LO's frequency stability as long as its deviation is within the measurement bandwidth of the receivers of the network analyzer.

Group-delay measurements are based on phase measurements. The measurement procedure corresponds to the definition of group delay as the negative derivative of the phase with respect to frequency. For practical reasons, instead of measuring the differential coefficient of phase, VNAs measure the difference coefficient of forward transmission parameter S₂₁, using the phase information at two adjacent frequencies. This yields a good approximation to the desired group delay as long as the variation is reasonably linear between these two frequencies.

For non-frequency-converting devices such as filters and amplifiers, phase measurements of S₂₁ at two frequencies can be easily made. However, in frequency-converting devices such as mixers the phase between the input and output signal cannot be directly measured. This is because the input and output frequencies are different. Furthermore, the phase of the output signal is influenced not only by the component itself but also by phase and frequency fluctuations of the LO.

The common technique for phase and group delay measurement on mixers uses a reference mixer in the reference path of the VNA. This reference mixer employs the same LO as the DUT to reconvert the frequency of the reference signal to the frequency of the RF or IF measurement signal. This eliminates the influence of LO phase and frequency instabilities. A block diagram of this technique is shown in Fig. 2.

The standard reference mixer technique works well when the LO is accessible, which is often not the case for aerospace and defense systems. In these cases, VNAs using amplitude-modulated (AM) or frequency-modulated (FM) signals attempt to reconstruct the LO with an external synthesizer. These approaches are slow and have low dynamic range or incur problems with unstable LOs that make measurements, especially on frequency converters with multiple mixing stages, extremely difficult. The new technique from Rohde & Schwarz circumvents all of these problems (Fig. 3).

The new method measures the phase between both carriers at the input and the output of the device to calculate the group delay

t = (-1/360 deg.)( φ/ f)

where

Δ φ φ = φ2 φ1

The frequency difference ( f) between both carriers is called the aperture. To measure the phase difference of two carriers, the R&S ZVA series VNAs incorporate two digital receivers in each analog receiver to measure both signals simultaneously (Fig. 4). This technique is especially applicable to frequency-converting devices because frequency and phase instabilities of the device's LO are canceled out when calculating Δφ:

φ = (φ1out + φLO φ2out φLO) (φ1in φ2in)

In addition to group delay, the R&S ZVA also calculates the relative phase of the device by integrating the group delay, and calculates dispersion by differentiation of the group delay. Using a mixer with known group-delay characteristics as part of the calibration process allows absolute group delay to be measured. If only relative group delay is necessary, a mixer with flat group delay is sufficient for calibration.

A frequency converter with the following characteristics can illustrate the effectiveness of the group delay measurement technique (Fig. 5):

Swept RF and IF, fixed LO, and with IF = RF LO;
RF range of 5.37 to 5.47 GHz;
LO at 4.5 GHz; and
IF of 870 to 970 MHz.

To obtain accurate measurements, the two-tone signal must have a known frequency offset, which the four-port R&S ZVA series VNAs provide using both of their internal sources. The two-tone signal is generated using an external combiner or one of the R&S ZVA's internal couplers as the combiner. The two-tone signal runs via the reference receiver of port 1 to the input of the device.

The selected aperture is 3 MHz, which means that the frequency offset between both carriers is 3 MHz. The measurement bandwidth has to be smaller than the frequency offset in order to separate both tones from each other. Frequency instabilities or deviations of the embedded LO do not affect the measurement, as long as they remain within the measurement bandwidth. If the two tone spacing is very small, highselectivity filters (with steep rejection skirts) are used.

Calibration is performed with an ideal or known calibration mixer, which can be characterized with the R&S ZVA-K5 option. With this option the R&S ZVA measures absolute phase and group delay of mixers. Absolute group delay is often not required, but only relative group delay and group delay ripple. In these cases, a mixer with linear phase and flat group delay is sufficient for calibration purposes.

The results using S-parameters and the two-tone technique to measure a bandpass filter are compared in Fig. 6. The red trace shows group-delay results derived from a conventional S-parameter measurement of the filter (in non-frequencyconverting mode). The blue trace shows group-delay measurements using the two-tone technique. The deviation between these two measurements is negligible.

The new Rohde & Schwarz two-tone measurement technique is designed to measure group delay and relative phase on mixers and converters without requiring access to the LO. It is immune to phase or frequency instabilities of the embedded LO, requires a minimum of additional hardware, and is simple to perform. Rohde & Schwarz, Inc., 8661A Robert Fulton Dr., Columbia, MD 21046-2265; (410) 910-7800, FAX: (410) 910-7801, e-mail: [email protected], Internet: www.rohde-schwarz.com.