Simple Noise Reduction Tool

 

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.

 

6 DB amplifier

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. 

Differential Amplifier

 

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.

 

Zero Ground Gain

 

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.

Gain 100 Amplifier

 

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?

Telecom Conference Bridge

 

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:

Vout1 =                   G2 * V2 + G3 * V3  + G0 * V0

Vout2 = G1 * V1                    + G3 * V3  + G0 * V0

Vout3 = G1 * V1 + G2 * V2                     + G0 * V0

 

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.

 

Summary

 

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 Gain Ga.

Minimize G0 and Ga by altering the Signal Gain Signs

If G0 is large, consider a differential approach       

Conclusion

 

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.