“Noise Analysis for High Performance Amplifiers”
Understanding Different Descriptions of Noise
Probably the most difficult aspect of amplifier noise analysis is the myriad of descriptions used
by the industry for the same underlying noise phenomenon. Different specification
requirements can lead engineers into describing noise in many different ways. A few of these
options are:
1) Spot or integrated noise
2) Input or output referred noise
3) Noise power or noise voltage and currents
4) Noise figure and/or noise temperature
Which form is used for each of these selections depends on what you are trying to accomplish.
Spot noises are almost always used in calculating total noise since there is normally a common
system bandwidth that will determine the integrated noise. Input noise is of interest for
developing the input Signal to Noise ratio while output noise, especially integrated noise, is of
interest when comparing the nose level to the ½ LSB (Least Significant Bit) of an ADC (analog to
digital convertor). Computations for developing equivalent noises considering multiple noise
sources are almost always defined in terms of noise voltages and noise currents. Noise figure
and noise temperature are amplifier input noise descriptions common to the RF and
communications field.
Figure 1 Non-inverting amplifier configuration with every noise source specified
An example computational flow will illustrate how these various descriptions fit together.
Taking the equivalent input spot noise voltages and currents as the starting point for any
description of noise (see Figure 1), an equivalent output spot noise power may be computed by
taking each voltage and current to the output through its appropriate gain and combining them
as the sum of squared terms. Noise current terms always include an impedance in their gain
expression to get all terms into squared voltage expressions. Strictly speaking, we should be
developing these powers across some resistance. However, in all subsequent expressions, the
resistances drop out and we are left dealing with voltages, currents, and gains squared. In
general, the separate noise sources are taken to be uncorrelated which is why we can combine
them by simply adding their component powers. Having computed the total output noise
power, the equivalent output spot noise voltage is obtained by taking the square root of this
expression.
For this spot noise voltage at the output, all other noise descriptions may be derived. The
integrated output noise voltage is obtained by multiplying the spot nose by the square root of
the noise power bandwidth NPB (which we will discuss at length in the coming weeks). This
yields an RMS noise voltage at the output for that bandwidth. Taking this voltage times 6 will
yield the approximate peak-to-peak voltage swing that would be seen on an oscilloscope for
this NPB. Adjusting the scope bandwidth illustrates the importance of noise power bandwidth
quite well.
Equivalent input spot noise voltages can be derived by taking this output spot noise voltage and
dividing by the voltage gain (from whatever input point you choose to define) to the output.
This is normally called “input referring” the output noise. Again, multiplying by the noise power
bandwidth will yield the input referred integrated noise. This is normally left as an RMS value
(as opposed to a peak-to-peak noise). With an equivalent input noise voltage derived, the Noise
Figure is developed by comparing this amplifier contributed noise to the source resistor noise.
In general, remember that computations combining noise sources together must be done with
squared voltages, currents, and gains. Getting back to voltage or current is simply the square
root of the sum of squared terms expressions. Integrated noise is computed by multiplying
noise power bandwidth (NPB) by the spot noise power (the sum of squared terms), or by
multiplying the square root of the NPB by the noise voltages or currents.
A CADEKA High Performance Amplifier Noise Analysis
For devices as flexible as CADEKA high performance amplifiers (either high frequency (CLC2005,
CLC2000, CLC4601, etc. or high precision (CLC1200, CLC 1003, etc.) one of the primary goals in
specifying the noise is to do it in a way that provides enough information as to predict the noise
performance under any set of operating conditions. The best way to do this is to define an
equivalent non-inverting input noise voltage and input noise currents for the non-inverting and
inverting inputs. These are defined as spot noise voltages and currents over frequency,
although in most applications, only the relatively constant high frequency (flatband) value is of
any interest. These three terms form the most elemental of common denominators for the
remaining types of noise descriptions. In any real measurement or applications, the resistors
used to operate the amplifier correctly will also contribute noise. Although often times
neglected, these can make a significant noise contribution in some cases and must be
considered for any complete noise analysis.
Figure 2 Non-inverting Noise Sources
With all of the contributing noise sources defined, an output spot noise voltage may be found
by using superposition for each of those sources. As with any other linear analysis, each noise
source is considered separately by opening all other noise current sources. Each source’s
contribution to the output noise is taken as the voltage squared generated by that source at the
output. Figure 2 show the contribution to the output of the noise sources appearing at the noninverting input. Note also that we are assuming an infinite input impedance at the noninverting node. This yields a gain of 1 to the non-inverting input for each voltage noise source
and a gain of RT for the non-inverting current noise. Each of these is squared and referred to the
output by multiplying by the non-inverting voltage gain squared. Figure 3 show the output
noise power contributions for the noise terms on the inverting side of the amplifier circuit.
Figure 3 Inverting Noise Sources
Of course, when evaluating the overall performance of a high performance amplifier (whether
it is a high frequency or high precision amplifier), each of the above parameters should be well
specified and understood and accounted for in the overall system level error budget.
Remember, while the data sheet specifications are helpful in the selection and specification of
an amplifier that will work within the required error budget, the designer will generally need to
individually measure each of the above parameters- within the real-life circuit/system level
environment, for optimal design.
Kai ge from CADEKA
(www.cadeka.com)