Sensitivity and Noise - Spectrum Analysis Basics

Sensitivity

One of the main uses of a spectrum analyzer is to search for and measure low-level signals. The ultimate limitation of such measurements is the noise generated by the spectrum analyzer itself. This noise, generated by the random electronic motion of various circuit elements, is amplified by the analyzer's multiple gain stages and appears as a noise signal on the display. This noise is often referred to as the displayed average noise level, or DANL, in the spectrum analyzer. (Displayed average noise level is sometimes confused with "sensitivity." Although they are related, they do not mean the same thing. Sensitivity is the minimum signal level that can be measured for a given signal-to-noise ratio (SNR) or bit error rate. It is a common specification of radio receiver performance. Spectrum analyzers are always given in DANL.) The noise power seen in DANL is a combination of thermal noise and the noise figure of the spectrum analyzer. Although some techniques allow the measurement of signals slightly below DANL, DANL always limits our ability to measure low-level signals.

Let us assume that a 50 ohm termination is connected at the input of the spectrum analyzer to prevent other signals from entering the analyzer. This passive termination generates a small amount of noise energy kTB, where:

k = Boltzmann constant (1.38 x 10–23 joule/K) T = temperature (K)

B = Noise bandwidth (Hz)

Since the total noise power is a function of the measurement bandwidth, the values ​​are usually normalized to a 1 Hz bandwidth. Therefore, the noise power density at room temperature is -174 dBm/Hz. When this noise reaches the first gain stage of the analyzer, the amplifier amplifies it along with its own noise.

当噪声信号继续通过系统时，由于幅度足够高，以致后续增益级产生的噪声对总噪声功率仅仅贡献了一小部分。注意在频谱分析仪的输入连接器和第一级增益之间会存在输入衰减器以及一个或多个混频器，这些元器件都会产生噪声。不过它们产生的噪声正处于或接近绝对最小值 -174 dBm/Hz，所以不会对进入第一增益级并被放大的噪声有显著影响。

Although the input attenuator, mixer, and other circuit elements between the input connector and the first gain stage have a small effect on the actual system noise, they have a significant effect on the analyzer's ability to display low-level signals because they attenuate the input signal; that is, they reduce the signal-to-noise ratio and thus reduce sensitivity.

With a 50 ohm load at the input of the spectrum analyzer, we can determine DANL by simply noting the noise level indicated on the display. The level shown is the noise floor of the spectrum analyzer itself. Signals below this level are obscured by the noise and cannot be observed. However, DANL is not the actual noise level at the input, but the effective noise level. The analyzer display is calibrated to reflect the signal level at the input, so the noise level shown represents the imaginary or effective noise floor at the input.

The actual noise level at the input is a function of the input signal. In fact, sometimes the noise is the signal of interest. Like any discrete signal, it is easier to measure when the noise signal is above the effective (displayed) noise floor. The effective noise floor at the input includes the input attenuator loss before the first gain stage, the mixer conversion loss, and other circuit component losses. We cannot change the mixer conversion loss, but we can control the RF attenuator. This allows us to control the input signal power into the first mixer stage and change the displayed signal-to-noise ratio. Obviously, the lowest DANL is achieved when the minimum (zero) RF attenuation is selected.

Since the input attenuator does not affect the actual noise generated by the system, some early spectrum analyzers simply displayed the noise at the same position regardless of the input attenuator setting. That is, the IF gain remains constant. In this case, the input attenuator will affect the position of the actual input signal on the display. When the input attenuation is increased, the input signal is further attenuated, the position of the signal on the display is lowered, and the position of the noise remains unchanged.

Starting in the late 1970s, spectrum analyzer designs took a different approach. In newer analyzers, the internal microprocessor changes the IF gain to compensate for changes in the input attenuator. So when the input attenuator is changed, the position of the signal on the analyzer input display does not change, only the displayed noise moves up or down. The reference level remains constant. As shown in Figure 1-1, as the attenuation increases from 5 dB to 15 dB to 25 dB, the displayed noise level rises while the signal level remains constant at -30 dBm. In either case, choosing the minimum input attenuation will give the best signal-to-noise ratio.

Figure 1-1. In a modern signal analyzer, the reference level remains constant when the input attenuation is changed.

Resolution bandwidth also affects the signal-to-noise ratio or sensitivity. The noise generated by the analyzer is random and has a constant amplitude over a wide frequency range. Because the resolution (or IF) bandwidth filter is located after the first gain stage, the total noise power that passes through the filter is determined by the filter bandwidth. This noise signal is detected and ultimately displayed. The random nature of the noise signal causes the displayed level to vary as follows:

10 log (BW2/BW1)

In the formula

BW1 = Start resolution bandwidth

BW2 = Stop resolution bandwidth

So if you change the resolution bandwidth by a factor of 10, the displayed noise level will change by 10 dB, as shown in Figure 1-2. For continuous wave signals, using the smallest resolution bandwidth provided by the spectrum analyzer will give the best signal-to-noise ratio or sensitivity. (Wideband pulse signals exhibit the opposite behavior; as the bandwidth increases, the SNR increases.)

Figure 1-2. Displayed noise level changes as 10 log (BW2 /BW1 )

A spectrum analyzer displays the signal plus noise. A low signal-to-noise ratio will make the signal difficult to discern. As mentioned earlier, a video filter can be used to reduce the amplitude fluctuations of a noisy signal while not affecting the amplitude of a constant signal. Figure 5-3 shows how a video filter improves the ability to discern low-level signals. Note that a video filter has no effect on the average noise level, so strictly speaking it does not affect the analyzer's sensitivity.

In summary, for narrowband signals, the best sensitivity and signal-to-noise ratio can be obtained by selecting the smallest resolution bandwidth and the smallest input attenuation. We can also set the smallest video bandwidth to facilitate observation of signals at or near the noise level. Of course, choosing a narrow resolution bandwidth and video bandwidth will increase the scan time.

Noise Floor Extension

虽然通过设计适合的硬件和选择恰当的元器件可以降低分析仪的固有本底噪声进而显著改善动态范围，但是在实际应用中仍存在着一些限制。还有一种方法可显著改善动态范围。通过全面的信号处理和其他技术创新，可对信号分析仪中的噪声功率进行建模并将其从测量结果中删除，从而降低有效噪声电平。在高性能 X 系列信号分析仪中，这项操作被称为本底噪声扩展（NFE）。

In general, if the noise power component of the analyzer can be accurately determined, the noise power can be subtracted from the results when making various spectrum measurements. Examples include spectrum measurements such as signal power or band power, ACPR, spurious, phase noise, harmonics, and intermodulation distortion. Noise reduction techniques do not improve the performance of vector analysis operations such as signal demodulation or time domain display of signals.

Figure 1-3. Video filtering makes low-level signals easier to discern.

Keysight Technologies has demonstrated its expertise in noise reduction technology, with its vector signal analyzers offering trace math to remove analyzer noise from spectrum and band power measurements (Keysight’s X-Series signal analyzers also offer similar trace math capabilities).

Although this feature is slightly awkward to use, it is very effective. It involves disconnecting the signal from the analyzer, measuring the analyzer noise level through heavy averaging, and then reconnecting the signal and using trace math to get and display the correct result. The analyzer noise power must be remeasured every time the analyzer configuration (center frequency/span, attenuation/input range, resolution bandwidth) is changed.

高性能 X 系列分析仪显著改善了这项测量技术，使之适用于多种测量场合。工程师在对分析仪进行校准时，会测量决定分析仪本底噪声的重要参数，然后用这些参数（以及当前的测量信息，如分析仪温度）构建分析仪本底噪声的完整模型，包括分析仪配置和工作条件发生变化时的模型。随后，分析仪会从频谱和功率测量结果中自动减去仪表噪声功率成分。这个处理过程称为本底噪声扩展，通过“ModeSetup（模式设置）”菜单里的按键启用。图 1-4 显示了一个实例。

The effect of NFE is manifested in several ways. The displayed average noise level (DANL) of the analyzer will typically decrease by 10 to 12 dB at low frequencies (below 3.6 GHz) and by about 8 dB at high frequencies (above 3.6 GHz). Although the displayed noise level will be reduced, this is only because the analyzer's noise power has been removed. Therefore, if the analyzer's noise power is a large percentage, the displayed signal power will be significantly reduced, but if it is not, the reduction will not be much.

With NFE enabled, the high-performance X-Series signal analyzers make more accurate measurements, whether of discrete signals or the noise floor of a source. NFE can be used with all spectrum measurements (whether RBW or VBW), any type of detector or averaging function.

Figure 1-4. Expanded view of the noise floor of harmonics

Noise Figure

Many receiver manufacturers specify receiver performance in terms of noise figure rather than sensitivity. As we will see later, the two specifications are convertible. A spectrum analyzer is a receiver, and we will study noise figure based on a sinusoidal input signal.

Noise figure is defined as the degradation of the signal-to-noise ratio when a signal passes through a device (in this case, a spectrum analyzer). We can express the noise figure as:

In the formula

F = Noise figure expressed as a power ratio (or noise factor)

Si = input signal power

Ni = true input noise power

So = output signal power

No = Output noise power

For a spectrum analyzer, this expression can be simplified. First, the output signal is the input signal multiplied by the analyzer gain. Second, since the signal level at the output (indicated on the display) is the same as the level at the input (on the input connector), the analyzer gain is 1. So after substitution, cancellation, and rearrangement, the expression becomes: