Amplifier Noise

Although the noise characteristics of a power amplifier are not as critical as those of a preamp, it is still important to achieve low noise because there is no volume control in the power amplifier to reduce noise from the input stage under normal listening conditions. This is particularly so when the amplifiers are used with high-efficiency loudspeakers. Power amplifier noise is usually specified as being so many dB down from either the maximum output power or with respect to 1 W. The former number will be larger by 20 dB for a 100 W amplifier, so it is often the one that manufacturers like to cite. The noise referenced to 1 W into 8 W (or, equivalently 2.83 V RMS) is the one more often measured by reviewers.
The noise specification may be unweighted or weighted. Unweighted noise for an audio power amplifier will typically be specified over a full 20 kHz bandwidth (or more). Weighted noise specifications take into account the ear’s sensitivity to noise in different parts of the frequency spectrum. The most common one used is A weighting, illustrated in Picture 1. Notice that the weighting curve is up about +1.2 dB at 2 kHz, whereas it is down 3 dB at approximately 500 Hz and 10 kHz.

The noise arising from different sources is usually assumed to be uncorrelated. For this reason, it adds on a power basis. This means that noise voltage adds up on an RMS basis as the square root of the sum of the squares of the various sources. Two noise sources each 10 µV RMS will add to 14.1 µV RMS. Two noise sources, one 10 µV and the other 3 µV will sum to 10.44 = µV. This shows how a larger noise source will tend to dominate over a smaller noise source.

Noise Bandwidth

Most noise sources have a flat noise spectral density, meaning that there is the same amount of noise power in each hertz of frequency spectrum. This means that total noise power in a measurement is proportional to the bandwidth of the measurement being made. This gives rise to the concept of noise bandwidth. A perfect brick-wall filter would have a noise bandwidth equal to its signal bandwidth. Because real filters roll-off gradually, the noise bandwidth is slightly different than the 3 dB bandwidth of a filter (often slightly more).

Noise Voltage Density

White noise has equal noise power in each hertz of bandwidth. If the number of hertz is doubled, the noise power will double, but the noise voltage will increase by only 3 dB or a factor of 2. Thus noise voltage increases as the square root of noise bandwidth, and noise voltage is expressed in nanovolts per root hertz nV/sqrt(Hz). There are 141 sqrt(Hz) in a 20 kHz bandwidth. A 100 nV/sqrt(Hz) noise source will produce 14.1 µV RMS in a 20 kHz measurement bandwidth.
As an aside, so-called pink noise has the same noise power in each octave of bandwidth. Pink noise is usually employed in certain test measurements. Pink noise is created by passing white noise through a low-pass filter having a 3 dB per octave roll-off slope.

A-Weighted Noise Specifications

The frequency response of the A-weighting curve is shown on Picture 1. It weights the noise in accordance with the human ear’s perception of noise loudness. The A-weighted noise specification for an amplifier will usually be quite a bit better than the unweighted noise because the A-weighted measurement tends to attenuate noise contributions at higher frequencies and hum contributions at lower frequencies. A very good amplifier might have an unweighted signal-to-noise ratio of –90 dB with respect to 1 W into 8 W, while that same amplifier might have an A-weighted SNR of 105 dB with respect to 1 W. The A-weighted number will sometimes be 10-20 dB better than the unweighted number.

Picture 1: A-weighting frequency response

Power Supply Noise

The power supply rails in any amplifier are often corrupted by numerous sources of noise. These may include random noise and other noises like power supply ripple and EMI and program-dependent noise from the output stage. The power supply noise can get into the signal path as a result of the signal circuit’s limited power supply rejection ratio (PSRR).
There are two important ways to control power supply noise. The first is to do a better job filtering the power supply rails. This is especially effective for power supply rails that provide power to low-level circuits. The second is to employ circuit topologies that have inherently high PSRR. The ability of a circuit to reject power supply noise usually decreases as the frequency of the noise increases. In other words, PSRR degrades at high frequencies. Fortunately, it is often possible to do a more effective job of filtering the power supply rails at higher frequencies.

Resistor Noise

All resistors have noise. This is referred to as Johnson noise or thermal noise. It is the most basic source of noise in electronic circuits. It is most often modeled as a noise voltage source in series with the resistor. The noise power in a resistor is dependent on temperature. It's determined as:

Pn = 4kTB [W]

k - Boltzman’s constant (k = 1.38 × 10^–23 J/°K);
T - temperature in °K (300°K @ 27°C);
B - bandwidth in hertz [Hz];

So, the resistor noise power density per Hertz, at temperature of 27°C (300°K) is pn = 1.66 × 10^–20 [W/Hz].

The open-circuit RMS noise voltage across a resistor of value R is simply:

en = sqrt(4kTRB)

or, en = 0.129 nV/sqrt(Hz) per sqrt(Ω) Noise voltage for a resistor thus increases as the square root of both bandwidth and resistance. A convenient reference is the noise voltage of a 1 kΩ resistor: 4.1 nV/sqrt(Hz). From this the noise voltage of any resistance in any noise bandwidth can be estimated.

BJT (Shot) Noise

Bipolar transistors generate a different kind of noise. This noise is related to current flow and the discreteness of current. This is called shot noise and is associated with the current flows in the collector and the base of the transistor. The collector shot noise current is usually referred back to the base as an equivalent input noise voltage in series with the base. It is referred back to the base as a voltage by dividing it by the transconductance of the transistor. Once again, the resulting input-referred noise is usually measured in nanovolts per root hertz.
The shot noise current is usually stated in picoamperes per root hertz [pA/sqrt(Hz)] and has the RMS value of:

Ishot = sqrt(2qIdcB)

q - 1.6 × 10^–19 Coulombs per electron;
B - bandwidth in Hertz;

It is easily seen that shot noise current increases as the square root of bandwidth and as the square root of current. An 1 mA collector current flow will have a shot noise component of 18 pA/sqrt(Hz).
The transconductance of a BJT operating at 1 mA is 38.5 mS. Dividing the shot noise current by gm we have input-referred noise en = 0.47 nV/sqrt(Hz). According to the equation for en, we can see that this is the voltage noise of a 13 Ω resistor. At the same time, notice that re’ for this transistor is 26 Ω. The noise voltage for a 26 Ω resistor is 0.66 nV/sqrt(Hz). The input-referred voltage noise of a transistor is equal to the Johnson noise of a resistor of half the value of re’. This is a very handy relationship.

JFET Noise

JFET noise results primarily from thermal channel noise. That noise is modeled as an equivalent input resistor rn whose resistance is equal to approximately 0.6/gm. If we model the effect of gm as rs’ (analogous to re’ for a BJT), we have rn = 0.6rs’. This is remarkably similar to the equivalent voltage noise source for a BJT, which is the voltage noise of a resistor whose value is re’/2. The noise of a BJT goes down as the square root of Ic because gm is proportional to Ic, and re’ goes down linearly as well. However, the gm of a JFET increases as the square root of Id. As a result, JFET input voltage noise goes down as the 1/4 power of Id.