Calculate and measure noise values

Measuring noise gets you halfway to reducing its effects.

Brad Thompson, Contributing Technical Editor -- Test & Measurement World, 5/1/2001

For electrical engineers, the word “noise” evokes a broad range of natural and artificial electrical disturbances. Some of those disturbances come from within analog circuit components such as amplifiers. If you build and test analog circuits, then you need to minimize the effects of your circuit’s internal noise. First, though, you have to measure the internal noise. If you know how much noise a circuit generates, you’ll know how low a signal level it can reliably process.

Circuit components generate noise across the entire frequency spectrum. Thermal noise—sometimes called resistive noise, Johnson noise, or Nyquist noise—comes from random, temperature-dependent motions of charge carriers in any component that’s warmer than absolute zero. This truly random or “white” noise arises from unpredictable fluctuations in voltage or current.

You can measure noise in an analog circuit with a noise-figure meter. If you don’t have one, you can still get a reasonable noise measurement with a DMM, power meter, or scope. To measure random noise in a circuit, you can use a noise source that introduces a known noise signal into your UUT, which in this article I’ll assume is an amplifier. If you know the noise power going into an amplifier, you can measure its output and calculate the amplifier’s noise contribution to the circuit, called its noise figure.

Often, you focus on the noise in a frequency range of interest only and can ignore any noise outside that bandwidth. For a given measurement bandwidth, you’ll find an equal noise power anywhere in the source’s noise spectrum. For practical purposes, a noise source that includes frequency components well in excess of an amplifier’s bandwidth classifies as white noise.

Put noise to work

Every circuit has a noise figure, which defines the low limits of signals that a circuit can reliably process. You can calculate that noise figure over a specified bandwidth. Figure 1 shows a concept circuit consisting of a signal source with its output impedance, Z_s, driving a linear amplifier of 1-Hz bandwidth and an input impedance, represented by Z _o.

To calculate the amplifier’s noise, you must first measure its gain over the bandwidth of interest. Set the signal source to produce a sine wave with a frequency within the bandwidth of interest. Measure the signal’s amplitude on both sides of the amplifier and calculate the amplifier’s gain in decibels. For simplicity, assume Z_i = Z_s= R_s. In the example, assume G_s, the amplifier’s gain, equals 20 dB.

Once you know the amplifier’s gain, you can use that value in an equation to calculate the amplifier’s noise. Replace the signal generator with a calibrated noise source. If you don’t have a calibrated noise generator, you can use a resistor (R_s) or other device. (See “Manufacture measurement noise,” for noise source options.) The noise power (–174 dBm) from resistor R_s depends on its temperature, resistance, and a specified bandwidth. You can use the general form of the equation in your calculations:

 where:

k = Boltzmann’s constant (1.374 x 10^-23 J/K)
T = temperature in Kelvin (°C + 273.16),
R_s = resistance in ohms
B = bandwidth

Room temperature measures about 290 K. (See the link above for derivation details of this and other equations relating to noise and noise figures.)

An ideal noiseless amplifier delivers output power, P_nn:

P_nn t (power from noise resistor R_s) +  (bandwidth of interest/1 Hz) + G_s
P_nn t (–174 dBm + log(1)) R 20 dBm
P_nn t –174 dBm + 0 + 20 dBm = –154 dBm

But real amplifiers produce noise. Suppose you measure –148 dBm at the amplifier’s output while its input comes from a calibrated noise source with a known power. The 6-dB difference between the calculated (–154 dB) and measured noise power (–148 dB) defines the amplifier’s noise figure, the amount of noise that the amplifier contributes to the circuit. (Ref. 1)

noise figure = measured power – calculated power
noise figure = –148 dBm – (–154 dBm) = 6 dB 

Figure 1. Use a calibrated signal source to measure an amplifier’s output and compute its gain (switch position 1). Use a noise source (Rs) to measure and compute the amplifier’s noise (switch position 2).

I mentioned that you need to measure an amplifier’s noise power to calculate its noise figure. Several types of dedicated and general-purpose instruments can measure noise power as well as noise figure. A measurement instrument should respond to noise power and offer a bandwidth at least 10 times that of a UUT’s noise bandwidth.

A noise-figure meter resembles a conventional RF receiver, but it has controllable bandwidth and an accurate power-level detector. A noise-figure analyzer adds swept-frequency capabilities. Today’s noise-figure meters and analyzers typically include features such as adjustable bandwidth, self-calibration, averaging displays, and others that simplify noise measurements.

If you don’t have a noise-figure meter or analyzer, you can use an AC voltmeter or a power meter to measure a UUT’s noise output power from which you can calculate noise figure. If you use a voltmeter, you must calculate power from the measured voltage and the circuit’s load.

The application in Figure 2 depicts a typical measurement circuit. In such a circuit, an analog display’s inherent time constants may make it easier to read than rapidly changing digits. But most modern digital instruments include averaging, so the displayed values should remain fairly stable. Remember, any average—digital or analog—suppresses peaks in a signal.

Figure 2. A rudimentary noise-measurement circuit uses basic building blocks.

You can also get a rough noise measurement with an analog oscilloscope or a DSO that emulates an analog scope. To make the measurement, you exploit the analog scope’s phosphor persistence and use your visual perception.

This technique uses two scope channels to measure the random (Gaussian) noise at any point in a circuit. You can use one channel and roughly measure the peak-to-peak noise in your circuit, but you will get a more accurate measurement with two channels.

a)

b)

c)

Figure 3. a) To measure a UUT’s noise, connect its output to both channels of a calibrated dual-trace analog scope. b) Adjust the position of one channel until the dark band disappears. c) Set both scope channels to ground and note the graticule distance between them.

Connect two scope probes to the same point in your circuit. Set both channels to the same range and select alternate-sweep mode and connect both channel probes to the UUT. Move the two traces apart vertically until you see a dark band between them (Figure 3a). Next, adjust the position of one channel until the overlapping noise from the two traces fills the dark band. (Figure 3b).

Remove the signal by setting both channels to “ground” (Figure 3c). Measure the distance (in graticule units per division) between the noise-free baseline traces. In my measurement, the distance is approximately 2.2 divisions. Multiply the distance by the volts/division settings and you have the circuit’s random noise.

For best results, make sure that no DC offset voltage enters either scope channel. To eliminate DC offset voltages, use AC coupling on both scope channels. A no-signal, floating-input trace won’t change position when you change gain ranges or select “input ground.”

Don’t overdrive the scope’s trace intensity. Frequently glance away from the screen while adjusting trace position so your eyes will let you just barely eliminate the dark band between the noise waveforms (Refs. 3, 4).

For more information about the varieties of noise and their myriad effects, download a Word document that refers to more books and Web sites. T&MW

References

1. See www.its.bldrdoc.gov/fs-1037/dir-024/_3560.htm for a definition of noise figure, also called noise factor.

2. Optimizing RF and Microwave Spectrum Analyzer Dynamic Range, Application Note 1315,
Agilent Technologies, Santa Clara, CA. Download at literature.agilent.com/litweb/pdf/5968-4545E.pdf.

3. Gruchalla, Michael E., “Measure Wide-Band White Noise Using A Standard Oscilloscope,” EDN, June 5, 1980. p.157.

4. Franklin, Gary, and Troy Hatley, “Don’t Eyeball Noise,” Electronic Design , November 22, 1973. p. 184.

Brad Thompson has been writing for Test & Measurement World since 1986. Currently, he serves as a Contributing Technical Editor and works as an independent electronics consultant and writer. E-mail him c/o T&MW: brad@tmworld.com.