Reducing Noise is one of many
challenges that a Designer encounters. There are many factors that
contribute to noise. The literature can be very confusing. Which
tool will work for your application? Here’s yet another tool.
If you model your system as a
linear system, then the output noise is the product of the magnitude of the
noise source times the gain from the noise source to the output. There
are hence two components that contribute to the output noise: The
magnitude of the noise source and the circuit gain from the noise source to the
output.
Many articles have described
techniques for reducing the noise source magnitude. This often involves
reducing the power supply impedance by using multiple capacitors of different
types.
The second method is to
reduce the circuit gain from the noise source to the output. This page
describes a simple technique to reduce the noise gain. The technique is
applicable to system design, very easy to use, and virtually
unknown.
What is it?
Alter the sign of the signal
gain.
In many applications the input
signal is AC coupled and the sign of the signal gain is not important.
For example, if an amplifier is needed to boost the signal by 6 DB, you can use
an inverting amplifier with a gain of minus two or a non-inverting amplifier
with a gain of plus two. Which would you choose?
Hint : One choice will couple about 10DB less noise into the
output.
If you can alter the signal
gain sign, how do you decide which is best?
There are two things you want
to minimize:
The
gain from the circuit ground to the output (G0) and
The
op-amp circuit gain.
Minimizing the Ground Gain ( G0)
will reduce the amount of ground noise in the output.
Minimizing the circuit gain ( Ga) will provide more excess
gain, which will reduce distortion and improve power supply noise
rejection.
For most op-amps the
gain-bandwidth product is a constant. Reducing the circuit gain will
increase the bandwidth. Daisy’s Theorem says the
sum of the gains is always 1. For high frequencies the circuit gain will
decrease and the power supply gain will increase to maintain a sum of 1.
Reducing Ga will increase bandwidth, move the cut-off
frequency higher, and thus reduce the power supply gain.
Daisy’s
Theorem provides a simple way to get the Ground Gain, G0.
G0 = 1 – Sum( Signal Gains)
The amplifier gain (Ga), sometimes called the Noise Gain, is the gain from +
op-amp terminal to the output.
Ga = Sum ( Positive Gains )
Note that the Ground Gain
is just another signal gain. Don’t neglect it.
Let’s look at some
examples.
The signal gain can be -2
(inverting amplifier) or +2 (non-inverting amplifier).
For the Inverting
Amplifier
G0 = 1 – (-2) = 3
Ga = 3
For the Non-Inverting
Amplifier G0 = 1 – ( 2) =
-1 Ga = 2
In this case the
Non-Inverting Amplifier will add 3 times less ground noise to the output, a
10DB reduction when compared to the Inverting Amplifier. See the Technical Daisy page for a detailed analysis.
The amplifier gain Ga is less for the Non-Inverting Amplifier. This will
provide less distortion and better power supply noise rejection.
For large gains, the Ground
Gain (G0) is large. A common method to reduce G0 is to use a Differential
Amplifier, if inputs of opposite polarity are available.
A differential amplifier has
two inputs (V+,V-) with equal and opposite gains (G).
Vout = G
* V+ - G* V-
G0 = 1 – (G – G) =
1 Ga = G+1
For any signal gain, the
differential amplifier has a ground gain of 1.
The circuit gain is G +
1.
For large gains, the
differential amplifier has a significant advantage over a single input
amplifier.
You probably knew this.
This is simply a confirmation.
For noisy ground
environments, such as internal to ICs, differential amplifiers are preferred
since they don’t amplify ground noise.
Is it possible to have a
ground gain of zero?
Yes.
The simplest example is a
circuit consisting of a short wire connecting the input to the output.
The equation is
Vout = 1 *
V1
G0 = 1 - ( 1) = 0
and
Ga =1
Another example is a buffer
amplifier. The equations are the same.
What about large gains?
You can achieve Zero Ground
Gain by using differential inputs and setting the positive gain to be 1 greater
than the negative gain.
A gain 100 amplifier with
differential inputs can be created by setting the
gain from Vin+ to 50.5 and the gain form Vin- to -49.5. The K9
Design is shown and analyzed on the Examples Page.
The difference between this
amplifier and the differential amplifier is the lack of an op-amp input
connection to ground. K9 Design only adds a ground input if the sum of
the signal gains is not equal to +1. No input connection to GND creates
zero gain from GND to the output.
Differential amplifiers are
sometimes used to cancel common mode components of the input. In this
case the gains need to be precisely matched. This creates a ground gain
of 1.
In the previous examples
there was only one signal input.
What about multiple signal
inputs?
A telecom conference bridge
needs to combine the voice signals from multiple uses. Each user wants to
receive the signals from the other users. If there are 3 conferees, that
supply signals V1, V2, and V3 to the bridge, the bridge outputs are:
The signal gain magnitudes
are typically equal. Since this is audio, the sign does not matter.
A telecom system needs to
match impedances at the input and output. This yields
a voltage gain of one half at the input and at the output. To compensate
a signal gain of magnitude 4 is required. If we assume the signal gain
magnitude is 4, what sign should the signal gains be?
All gains are
positive
G0 = 1 - ( 4 + 4 ) =
-7
Ga = 8
All gains are negative
G0 = 1 - ( -4 - 4 ) = 9
Ga = 9
Gains have opposite
signs
G0 = 1 - ( -4 + 4 ) =
1
Ga = 5
Most conference bridge
designs use gains of the same polarity. This increases the noise
level.
Using opposite polarity
gains will also improve the stability of the conference. Trust me.
The same argument for mixed
gains can be applied to Audio Mixers.
An Executive summary is:
For a single input circuit,
use a non-inverting design.
When Mixing,
use Opposite Signs.
An Engineer summary is:
Calculate the Ground Gain,
Go and the Circuit
Minimize G0 and Ga by altering the Signal Gain Signs
If G0 is large, consider a
differential approach
Noise is a mayor concern in
Analog circuit design.
There are many techniques to
reduce ground noise. Use all of them.
Try to minimize the ground
gain and circuit gain by altering the signal gain signs.