Читать книгу Handbook of Microwave Component Measurements - Joel P. Dunsmore - Страница 122

The consideration of system noise floor is often not included in the specifications of measurement accuracy, under the assumption that noise effects can be eliminated with sufficient reduction in IF bandwidth or increase in averaging factor. While this is theoretically true, in many circumstances the increase in measurement time makes this impractical. In some situations, such as real‐time tuning of microwave filters, the IF bandwidth must be increased to achieve a real‐time update rate. The noise effects increase 10 dB for each 10× increase in IF BW, so it is a simple matter to compute the effective noise floor at any IF BW given a noise floor at some IF BW, typically 10 Hz.

There exist two distinct noise effects in S‐parameter measurements: noise floor and high‐level trace noise. The noise floor is easily understood as the effect of added noise at the input of the receiver, due to the noise figure of the VNA receiver. The coupling factor of the test port coupler reduces the measured signal further so that the effect of noise floor is more dominant. The effect of noise floor on a measurement can be determined by taking the RMS noise floor, converting it to an equivalent linear amplitude wave, and then adding it to the amplitude of the signal at the measured receiver.

The conversion to the linear b₂ noise is

(2.9)

Note that the raw measured noise floor on a VNA receiver will be the square root of the noise power, as the a and b waves are in units of square root of power.

Often, the noise floor of a VNA is expressed as a dBc value relative to a 0 dB insertion loss measurement. Of course, for a constant noise power in the receiver, the relative noise floor will depend upon the source drive power.

The RMS trace noise apparent on an S‐parameter trace can be computed by adding the RMS noise floor to the amplitude of the signal at the b receiver.

(2.10)

when the noise floor is sufficiently below the measurement of interest. Of course, when the noise floor is above the measured value, the measurement becomes meaningless.

Take, for example, a filter with 80 dB of insertion loss (S21 = −80 dB), with a drive power from the source of 0 dBm, a VNA with an RMS noise floor of −127 dBm in a 10 Hz bandwidth. If it is measured using a 10 kHz IF bandwidth, as shown in Figure 2.32, the trace noise due to noise floor at any insertion loss can be computed.

Figure 2.32 Effects of noise floor on an S21 measurement.

The effective noise floor is 30 dB greater than the 10 Hz spec, for a level of −97 dBm. The measured b₂ noise would be

(2.11)

The output signal is

(2.12)

The RMS trace noise level would then be

(2.13)

This value is close to the measured trace noise, shown as trace statistics computed near Marker 1 on Figure 2.32 and displayed as SDEV = 1.24 dB (trace statistics measures the variation of signal of a trace, and in this case the computation is restricted to be a 5% region near the marker position). Thus, one would see substantial noise on the filter stopband measurement. The RMS trace noise represents one standard deviation of noise. For this example, about 21 points are used to compute the trace noise near the marker. One would expect a peak‐to‐peak trace noise of about four standard deviations in the worst case or approximately 4.6 dB of peak‐to‐peak noise on a typical measurement. However, since noise can take on any value for any single instance, the RMS value is almost always used when describing noise‐related values. As the S‐parameter signal rises above the noise floor of the VNA, trace noise diminishes at a rate of about three times (in dB) for each 10 dB increase in signal level. But this 3‐for‐10 reduction doesn't continue at high signal levels.

A second cause of trace noise in a measurement is called high‐level trace noise. At high signal levels, the noise from the source signal, typically due to the phase noise of the source, can rise above the VNA noise floor and dominate the trace noise in the measurement. Further, if the source in the VNA has substantial internal amplification, the broadband noise floor from the source can dominate the phase noise far from the carrier. In this region, the trace noise stays approximately the same as the S‐parameter signal increases. Consider the trace noise on the skirt of a filter: when the signal through the filter is sufficiently high, the trace noise on the measurement decreases as the signal level rises above the noise floor, until the source phase noise or pedestal noise, as it is sometimes called, becomes dominant. Above this level the trace noise stays constant as a dBc level even as the S‐parameter loss diminishes. The problem of high‐level trace noise is more commonly found on older VNAs where phase noise was typically worse than that of stand‐alone signal sources due to the difficulty of integrating sources internally. The problem is also seen on more modern VNA systems at mm‐wave frequency, where multipliers are used to increase the source frequency. With each 2x multiplication of frequency, the phase noise increases by 6 dB. These problems are typically seen only at high power levels because the use of attenuators for power‐level control reduces the source signal and the phase noise in the same manner.

Figure 2.33 shows the phase noise of a VNA source as it is increased to where the phase noise is higher than the noise floor. The memory trace, shown in light gray, is for a power level of −10 dBm. At this level phase noise is below the receiver noise floor. The dark trace shows the phase noise when the source power is increased to +10 dBm. Here the phase noise is about 15 dB above the noise floor and will limit the high‐level trace noise. This data was measured with a 10 kHz resolution bandwidth (RBW), so the actual maximum phase noise is about −110 dBc Hz⁻¹ at offsets below about 50 kHz.

Figure 2.33 VNA source signal where phase noise rises above noise floor.

Figure 2.34 shows a plot of trace noise as a function of received power. In this normalized response, the trace noise limit is apparent in the high‐level region starting at about −10 dBm, where the trace noise no longer decreases directly as a function of increased signal level, indicated on the figure as the “Hi‐Level Trace Noise” region.

Figure 2.34 Example of trace noise decreasing with increased signal level, until high level noise limit is reached.