**Op-amp noise calculator.**

With this op-amp noise calculator you can calculate the noise production of an
op-amp amplifier design.

You can enter the parameters of the amplifier in the yellow coloured fields, and
then click the calculate buttons.

Much success with the op-amp noise calculator, hoping it is useful for you!

Below the calculator you will find more explanation about the calculations.

About this calculator

This op-amp noise calculator calculates for you the output noise of an op-amp
amplifier design.

The calculations are based on the noise parameters of the op-amp, and the
thermal noise generated in the resistors in the circuit.

These are the major noise sources in most of the amplifier designs.

There are however other types of
noise in electronic circuits which are not discussed here.

More info about all types of noise in electronic
circuits, can be found in this article by Texas
Instruments.

There are a lot of things which could be calculated about amplifiers,
concerning: bandwidth, output voltage swing, slew rate, offset voltage,
etcetera.

The subject of this calculator is however limited to: noise.

For instance, depending on the data you enter, you can get very high
output noise or signal output, which in practice can never be reached because
they exceed the supply voltage of the op-amp.

So, only the noise is calculated, and for the rest you should keep an eye on it
yourself.

The explanations below only discuss the subjects
which are necessary to do the calculations.

There is a lot more to write about noise, but I omit this, because I don't want
to make this article more complex then it already is.

Every resistor will generate a certain noise voltage, this is caused by
thermal agitation of the electrons inside the resistor.

The resistor doesn't have to be in a circuit, or connected to a power supply,
the noise voltage is just always there.

The noise voltage (Vn) in a resistor can be calculated with the formula:

Vn = √ (4.k.T.B.R)

Where:

Vn = The noise voltage in Volt RMS.

k = Boltzmann's constant = 1.38 . 10^{-23} J/K

T = Temperature of the resistor in Kelvin (K)

B = Bandwidth of the measurement in Hertz (Hz)

R = Resistor value in Ohm

This formula is valid for noise frequencies up to 100 MHz.

Figure 5.

The noise voltage (Vn) can be considered as a voltage source in series with the
resistor (R).

You might measure the noise voltage across the two leads of the resistor, but
normally the amplitude of the noise voltage is in the microvolt range, so very
low.

The amplitude of the thermal noise is depending on temperature, if you cool the
resistor down to the lowest possible temperature of 0 K ( = -273.15 °C ) ,
the electrons are at rest, and there will be no thermal noise generated anymore.

**Bandwidth**

The thermal noise generated in a resistor has all frequencies in it, from 0
Hertz (Hz) to very, very high frequencies.

Up to 100 MHz, every Hertz of bandwidth contains an equal amount of noise power, in other words
it is "White noise".

However the circuit in which the resistor is used can limit the bandwidth of
the noise signal.

For instance, an audio amplifier has an - 3 dB frequency response of 20 - 20000
Hz.

Then it's bandwidth is (20000 - 20 =) 19980 Hz.

If we calculate the noise output of this amplifier, we can consider the
bandwidth of the noise to have the same bandwidth.

Now we want to measure the noise output of the amplifier with an audio spectrum
analyser, which we connect to the amplifier output.

And to our surprise we measure a lower noise level then calculated.

This is caused by the bandwidth of the audio spectrum analyser.

However it measures from 0 - 20000 Hz (or more), it measures only a small piece
of the spectrum (let's say 10 Hz wide) at one time, and then scan during some
time the whole spectrum.

So the spectrum analyser is reducing the bandwidth down to (in this case) 10 Hz,
which will reduce the noise level measured.

If we are measuring the noise level of an electronic circuit, both the circuit
and the measuring device can limit the bandwidth, and by this, the amplitude of
the noise
we measure.

**Noise in signal sources
**

A signal source can consist of a voltage source (Vs) with a series resistor (Rs), see figure 6.

The resistor Rs will generate a thermal noise voltage (Vn), which seems to be in series with the signal Vs

Figure 6.

At the output of the signal source, we can measure the noise of Rs added to
the signal voltage.

Now we are able to calculate the signal-to-noise ratio of the signal source,
with the following formula:

SNR_{dB}(source) = 20 log_{10} (A_{signal} /
A_{noise}).

Where:

SNR_{dB}(source) = The signal to-noise ratio of the source expressed in dB.

A_{signal} = The amplitude of the signal Vs

A_{noise} = The amplitude of the noise Vn

The signal source can also consist of a current source (Is) with a parallel
resistor, see figure 7.

Figure 7.

The current source (Is) with parallel resistor can be converted to a
voltage source (Vs) with series resistor, with the formula:

Vs = Is.Rs

The value of the resistor Rs stays the same.

The next step is to add the thermal noise voltage (Vn) of Rs, and we get the
same circuit as in figure 6.

We can also calculate here the signal-to-noise ratio as described.

In fact, we can not see or measure on the output of the signal source if
there is a voltage source (figure 6), or a current source (figure 7) inside.

In both situations the behaviour of the signal source is the same.

The conversion from current source to voltage source is just to make the
calculations easier.

**Op-amp noise**

On this webpage I discuss the noise generated in amplifiers which uses an op-amp
(operational amplifier).

All the resistors in the amplifier circuit will generate some noise, which will
appear at the output of the amplifier.

Also the op-amp itself will generate noise

Figure 8

In terms of noise, we can think of an op-amp as having four components in it,
which are:

- a noise free op-amp.

- a voltage noise source in series with the + input.

- a current noise source from ground to the + input

- a current noise source from ground to the - input.

In figure 8 we see these four components drawn within the dashed triangle,
which represents the actual op-amp.

The input voltage noise is in datasheets given in the unit
nV /√Hz.

This means this is the voltage when we measure in a bandwidth of 1 Hz.

In most applications we use more then 1 Hz bandwidth, and we should multiply by
the square root of the bandwidth to get the actual input voltage noise.

Example: the op-amp datasheet gives a input voltage noise of: 5 nV /√Hz.

We use this op-amp in an audio amplifier with a frequency range of 20 - 20000
Hz, so the bandwidth is 19980 Hz.

The square root of the bandwidth is: √19980 Hz = 141.35 √Hz.

Now the input voltage noise for this op-amp will be: 5 nV /√Hz
. 141.35 √Hz. = 706.75 nV.

We see the term √Hz has disappeared in the answer.

The voltage we get is the effective voltage, or RMS value.

An op-amp with low input voltage noise, is
especially preferred if the resistance of the signal source is low, up to some
kilo-Ohm.

If the resistance of the signal source is much higher, you can better use an
op-amp with low input current noise.

**Op-amp input current noise.**

The two input current noise sources of the op-amp are in datasheets specified in
pA /√Hz, and sometimes for very
low-noise devices in fA /√Hz

1 fA (femto-Ampere) = 0.001 pA (pico-Ampere).

For "voltage feedback" op-amp's (the ones discussed on this page), the input current noise for + and - input
normally have the same value, and in
the datasheet only one value is given, which is valid for both + and - input.

However the amplitude of the two current noises is equal, they are not related
to each other.

And we are not able to remove the noise by subtracting the two currents, as is
possible with DC input bias current.

Also with the input current noise we should
multiply by the square root of the bandwidth to get the actual current value.

This is just like we did with the input voltage noise.

Not always the input current noise of the op-amp
is given in the datasheet.

We can however calculate the minimal value of the input current noise from the
value of the input bias current with the formula:

In (input) = √(2.Ib.q).

Where:

In = input current noise in A/√Hz.

Ib = Input bias current of the op-amp in A.

q = Charge of one electron, which is 1.6 . 10^{-19} Coulomb

The next calculator will do this calculation for you:

The calculated value for the input current noise is the minimum possible
value, and only valid if the input of the op-amp is internally only connected to
one transistor base, of FET gate.

If the input of the op-amp is connected to more transistors or FET's, or has
some ESD protection circuit connected to it, the input current noise will be
(much) higher then calculated.

Noise gain factors

Every resistor in the amplifier circuit generate it's own noise, each of
these noises will appear at the output of the amplifier with a certain gain
factor.

Also the op-amp input voltage noise, and input current noises will reach the
amplifier output with a certain gain factor.

For finding the noise gain factors, take one noise source at a time, and imagine
all other noise sources are zero.

Then try to find out, how this single noise signal is amplified before it
reaches the amplifier output.

Well, I have already done this for you, and here comes the story:

**Noise gain factors for the non inverting amplifier:**

Figure 9.

First we look for the noise gain factor for the noise of resistor R1:

The voltage at the op-amp + input is zero, because we imagine Rs and R3 are not
generating noise at the moment, also signal Vs is zero.

The op-amp will always try to keep the + and - inputs at the same voltage, so
the - input is also at zero volt, and there is no voltage across R2.

The noise voltage in series with R1 will now reach the amplifier output with a
gain of 1, so:

**The noise gain factor for R1 is: 1.**

And now for resistor R2:

The op-amp + input is still at zero volt, so also the - input.

A noise voltage (Vn) in series with R2 will cause a current through R2 of Vn/R2, and this
current must then flow through R1, because the op-amp input does not take up
this current.

The voltage across R1 will then be: Vn. R1/R2.

And because one side of R1 is at zero voltage, the other side, which is the
amplifier output will show the noise of R2 with a gain of R1/R2.

**The noise gain factor for R2 is: R1/R2.**

The noise voltage generated in R3 first goes through a voltage divide, and is
divided by a factor Rs/(Rs+R3) before it reaches the op-amp + input.

Then the op-amp will amplify it with a factor 1+R1/R2.

**The noise gain factor for R3 is: (1+R1/R2).Rs/(Rs+R3).**

The noise gain for Rs is very similar to that of R3, only the voltage divider
is now dividing by R3/(Rs+R3).

**The noise gain factor for Rs is: (1+R1/R2).R3/(Rs+R3).**

The input voltage noise of the op-amp can be considered as being (internally in
the op-amp) in series with the + input of the op-amp.

As the + input of the op-amp is at zero voltage, the input voltage noise will
appear at the - input of the op-amp.

Here it causes a current through R2, which current will flow through R1.

**The noise gain factor for the op-amp's input voltage noise is: 1+R1/R2.**

Until now the gain factor formula's were without unit, it's just a number by
which we multiply a voltage to get another voltage.

The input current noise of the op-amp's + input is flowing out of the +
input, and goes through the parallel circuit of Rs and R3.

Rs and R3 parallel have a resistance of:
Rs.R3/(Rs+R3).

This causes a certain noise voltage at the + input of the op-amp.

And the op-amp amplifies this with a factor 1+R1/R2 to it's output.

**The noise gain factor for the op-amp + input current noise is: (1+R1/R2).Rs.R3/(Rs+R3)
.**

Please note that the unit of this gain factor formula is: Ohm (or Volt per
Ampere), which is
necessary because we convert Ampere to Volt, so we need to multiply by Ohm.

Now look at the input current noise coming out of the - input of the op-amp.

The + input is at zero volt, so also the - input.

This means all the noise current coming out of the - input will flow through R1,
and causes a voltage across R1.

**The noise gain factor for the op-amp - input current noise is: R1.**

Also here the unit is Ohm, which is necessary to convert Ampere to Volt.

Now we have discussed all the noise gain factors for the non inverting
amplifier.

**Signal gain for the non inverting amplifier:**

For the non inverting amplifier, the signal gain from Vs to amplifier output is:
**(1+R1/R2).R3/(Rs+R3).**

This is the same formula as the noise gain for Rs, which is logical because the
signal voltage (Vs) and the noise of Rs are series connected, so they appear
with the same gain at the amplifier output.

Please note, this is not the gain from amplifier input to amplifier output.

But from unloaded signal source (which is equal to Vs inside the signal source)
to amplifier output.

**Noise gain factors for the inverting amplifier:**

Figure 10.

For the inverting amplifier, the noise gain factors are in some cases more complex, I don't give here explanation, but just the formula's.

**The noise gain factor for R1 is: 1.**

**The noise gain factor for R2 is: R1/(R2+(Rs.R3/Rs+R3)).**

**The noise gain factor for R3 is: (R1/R2).Rp/(Rp+R3).**

Where: Rp = Rs.R2/(Rs+R2).

If R2 = 0, then the noise gain factor for R3 is: **R1/R3.**

**The noise gain factor for R4 is: 1+ R1/(R2+Rp).
**Where Rp = Rs.R3/(Rs+R3).

**The noise gain factor for Rs is: (R1/R2).Rp(Rp+Rs).**

Where Rp = R2.R3/(R2+R3).

If R2 = 0, then the noise gain factor for Rs is: **R1/Rs.**

**The noise gain factor for the op-amp's input voltage noise is: 1+
R1/(R2+Rp).
**Where Rp = Rs.R3/(Rs+R3). So the same formula as for the
R4 noise.

**The noise gain factor for the op-amp + input current noise is: R4.(1+
R1/(R2+Rp)).
**Where Rp = Rs.R3/(Rs+R3).

**Signal gain for the inverting amplifier**

For the inverting amplifier, the signal gain from Vs to amplifier
output is: **(R1/R2).Rp(Rp+Rs).**

Where Rp = R2.R3/(R2+R3).

If R2 = 0, then the signal gain is: **R1/Rs.**

This is the same formula as the noise gain for Rs, which is logical because the
signal voltage (Vs) and the noise of Rs are series connected, so they appear
with the same gain at the amplifier output.

**The function of resistor R4 in the inverting amplifier**

Now some explanation on the function of resistor R4 in the inverting amplifier.

In a lot of inverting amplifier designs the + input of the op-amp is directly
connected to ground, so R4 is 0 Ω.

Then R4 will cause no noise at the amplifier output, and also the + input
current noise of the op-amp will give no noise at the amplifier output.

Resistor R4 may however be added to reduce the DC offset voltage at the output
of the amplifier.

In this case we can place a capacitor with high enough capacitance across R4.

This will short circuit any noise to ground, while not affecting the DC
component.

For the noise calculations, we then can calculate with the value R4 = 0
Ω.

**Determining the total noise at the amplifier output**

In an op-amp amplifier, as we have seen, are several sources of noise, which
all causes some noise at the amplifier output.

Now we want to know the total noise at the amplifier output.

For doing this we take the square of each noise voltage, which is in fact
converting voltage to power.

Then we add all these squared values (so, we add the powers), and then take the
square root of the answer, which is converting power back to voltage.

So, total noise at amplifier output = √ (Vn1² +
Vn2² + Vn3² + Vn4² + etc. ..).

Where Vn1, Vn2, etc. represents the separate noise sources.

The noise of the signal source is also one of the noise sources, which (squared)
should be added.

If we want to reduce the noise output of the
amplifier, we should focus on the noise sources which produces the most noise at
the amplifier output.

If for instance one noise source gives 5 times more noise at the amplifier
output then any other noise source, then the squared value is 25 times higher.

This noise source is then very dominant over all the others, and reducing the
noise of the other sources will hardly have any effect on total noise output.

**Signal-to-Noise Ratio in dB (SNR _{dB})**

When you have a certain signal with noise on it, you can calculate the Signal-to-Noise Ratio expressed in dB.

The SNR

When SNR

When the SNR

When you express the signal and noise as voltages with a certain RMS amplitude (A), the SNR

SNR_{dB} = 20 log_{10} (A_{signal} /
A_{noise}).

When you express the signal and noise as powers (P) going to some load
resistor, then the SNR_{dB} can be calculated as:

SNR_{dB} = 10 log_{10} (P_{signal }/ P_{noise})

Both formulas give the same result.

In my op-amp noise calculator, signal and noise are expressed as voltages, so I
use the first formula.

The number 10 after the "log" means; you should take the 10 based logarithm.

**Noise figure (NF)**

The signal source has a certain SNR_{dB}.

When you amplify this signal with a noise free amplifier, the SNR_{dB}
would stay the same at the amplifier output.

However, in practice amplifiers are never noise free, and will add some noise to
the amplified signal.

This will cause the SNR_{dB} at the output of the amplifier
to be lower then the SNR_{dB} of the source.

The difference is the Noise Figure (NF) of the amplifier, and the unit is: dB.

NF = SNR_{dB} (source) - SNR_{dB} (amplifier output).

An ideal noise free amplifier will have a Noise Figure of 0 dB.

The NF is depending on resistance value and temperature of the source.

So if you change one of these things, while not changing anything to the
amplifier itself, the NF of the amplifier will change.

The unit dBV is a logarithmic voltage ratio of a signal to a reference of
1.00000 Volt RMS.

The signal level in dBV is equal to: 20 log_{10} (signal in
Volt RMS).

This means that a signal of 0 dBV is equal to exactly 1 Volt RMS.

**dBu**

The unit dBu is a logarithmic voltage ratio of a signal to a reference of
0.774596669 Volt RMS.

The signal level in dBu is equal to: 20 log_{10} (signal in Volt RMS /
0.774596669).

This means that a signal of 0 dBu is equal to 0.774596669 Volt RMS.

The signal level in dBu is always 2.218487499 dB higher then the value in dBV.