**Measurement of a Small Signal Near a Large Signal Using a Spectrum Analyzer**

**Morris Engelson JMS Consulting Portland, OR**

A number of factors are involved in determining whether a small signal can be measured in the presence of a larger signal using a spectrum analyzer. The type of signal involved has a significant impact. For example, the measurement results for a digitally modulated or pulsed carrier are quite different than for a sine wave. The effects of various spectrum analyzer specifications, such as sensitivity, or control settings, such as resolution filter bandwidth, are different for different signal types. This article focuses on the simple case of sinusoidal signals.

# Resolution Filter Shape Factor

It is understood that multiple sine-wave signals are separated, or resolved, for individual display and measurement when the 3 dB resolution bandwidth (RBW) filter is set at less than the frequency separation between signals. Thus, the RBW must be no more than 100 Hz to distinguish between, and individually measure, two sinusoids 100 Hz apart. However, this criterion applies only if the signals are of equal amplitude. The filter bandwidth becomes wider further down on the slope, or skirt, of the filter shape. This wider filter bandwidth will obscure a small signal next to a larger one unless the frequency separation is increased. Hence, the specification of the shape factor is defined as the ratio between the 60 and 3 dB filter bandwidths. Except for special performance needs, such as in electromagnetic interference measurements, resolution filters are based on the synchronous sections in cascade principle. The most commonly used filter consists of four sections in cascade, though five- and six-section filters are also used. This cascade configuration is sometimes known as a Gaussian-like filter because the shape becomes Gaussian as the number of cascaded filter sections goes to infinity. The shape factor ratio of 60 vs. 3 dB bandwidths for four-, five- and six-section and Gaussian filters is 12.7, 10.0, 8.6 and 4.5, respectively. This shape factor relationship means that a five-section filter, which is 1 kHz wide at –3 dB from the filter’s center frequency response, will be 10 kHz wide at –60 dB. A signal that is 60 dB smaller than an adjacent larger signal must be offset in frequency accordingly if it is to be recognized and measured separately. The reader can determine the appropriate frequency offset for any relative signal level difference in decibels and filter design from the expression [(1 + X2)1/2]n. For example, if a measurement is to be made on a signal that is 40 dB down in level from an adjacent sinusoidal signal with a spectrum analyzer that uses a four-section resolution filter, what is the bandwidth ratio of the –40 to –3 dB filter bandwidths? The voltage ratios are ÷2– and 100 for 3 and 40 dB, respectively. Hence, using this filter shape relationship for –3 dB yields [(1 + X2)1/2]4 = ÷2 thus X = 0.435. Setting the expression equal to 100 and solving for X yields 3.00 for the 40 dB bandwidth. These results mean that the 40 dB bandwidth is 3/0.435 = 6.9-times as wide as the 3 dB RBW.

# Phase Noise

Spectrum analyzer phase noise is another limitation on the ability to measure a small signal next to a larger one. In most spectrum analyzers, the phase noise sidebands extend beyond the resolution filter shape for the narrower bandwidths below approximately –40 dB. Hence, the limiting factor for these measurements is frequently the phase noise rather than the filter shape. Spectrum analyzer phase noise performance is specified using either a graph or tabulation of the noise level below the carrier in a 1 Hz bandwidth (dBc/Hz) at a particular offset from the main signal frequency. This phase noise level must be compared to the filter shape to determine the measurement limitation. For example, a six-section resolution filter is 8.6-times as wide at –60 dBc as at –3 dBc per the discussion on shape factor. (That is, a 100 Hz 3 dB bandwidth is 8600 Hz wide at –60 dBc.) The filter skirt is –60 dBc at an offset of 4300 Hz to either side of the signal. Therefore, a small signal 55 dB below a larger signal, which is 5 kHz offset from the large-signal frequency, should be easy to observe and measure. However, suppose the large signal is located at a frequency of 30 GHz. The phase noise may be no better than –70 dBc/Hz at a 5 kHz offset because phase noise degrades rapidly with increasing frequency. Therefore, the phase noise sideband is only 70– 10log100 = 50 dB below the carrier level using a 100 Hz filter bandwidth. Hence, a signal 55 dB down cannot be measured. The small signal must increase in level by 5 dB (from –55 to –50 dBc), the offset must increase or the RBW must be reduced to 10 Hz so that the phase noise will lower to –(70 – 10log10) = –60 dBc.

# Sensitivity Limitations

Sometimes the small-signal limitation is affected by both the large-signal level and the internal noise of the spectrum analyzer. For example, consider the measurement of a small signal 55 dB below a –60 dBm signal at 5 kHz offset, as discussed previously. The level of the small signal is –60 – 55 = –115 dBm. This signal cannot be observed or measured using a 100 Hz RBW if the sensitivity of the spectrum analyzer is –110 dBm at a 100 Hz filter bandwidth. To make the measurement, the spectrum analyzer noise must be reduced by utilizing a narrower bandwidth.

# Multiple-signal Factors

Additional problems arise when multiple large signals are present. Here, the result is affected by the spurious responses from the intermodulation of the large signals, which hide the small signal to be measured. The measurement limit can be computed from the intermodulation relationship

dBc = (n – 1)(I – S), where

dBc = amplitude difference between signals

n = intermodulation order number (usually set at n = 3)

I = third-order intermodulation intercept point of the spectrum analyzer

S = large-signal level

Thus, for a spectrum analyzer with a third-order intercept point of +10 dBm, the measurement limit for two –20 dBm signals is dBc = (3 – 1)(10 + 20) = 60 dB. Signals smaller than 60 dB below the large signals will be hidden by the intermodulation responses even though the filter shape or phase or sensitivity noise might permit a measurement.

**Conclusion** ** ** To determine the measurement limitations of a small signal in the presence of large signals, the resolution filter shape factor, instrument phase noise sideband level, sensitivity noise level and intermodulation spurious response level must be considered. This article has presented examples that demonstrate how this analysis is performed.

*Morris Engelson is consulting director for JMS Consulting, which is located in Portland, OR. He can be reached at (503) 292-7035. Additional information on spectrum analysis can be obtained from www.pcez.com/~jms.*