# Relationship between PSRR and gain

Wikipedia says that power supply rejection ratio (PSRR) is the ratio of output noise referred to the input vs noise at the power supply:

The PSRR is defined as the ratio of the change in supply voltage to the equivalent (differential) input voltage it produces in the op-amp

Good Quality Design of Analog Cmos Integrated Circuits by Razavi seems to say the same thing:

The power supply rejection ratio (PSRR) is defined as the gain from the input to the output divided by the gain from the supply to the output.

So the overall rejection from power supply to output vary with the closed-loop gain of the op-amp?

So an op-amp with +40 dB gain and 100 dB PSRR, with 0 dBV noise at the power supply would have -60 dBV noise at the output? The Wikipedia example seems to say that it would be -120 dBV instead, which I don't understand.

Is there also an output component of PSRR? Like if you lower the gain of the amp, the input referred noise would decrease, right? But is there then a constant component coupled from the power supply through the output stages that starts to dominate?

Analog Devices MT-043, on the other hand, says:

PSRR or PSR can be referred either to the output (RTO) or the input (RTI). The RTI value can be obtained by dividing the RTO value by the amplifier gain. In the case of the traditional op amp, this would be the noise gain. The data sheet should be read carefully, because PSR can be expressed either as an RTO or RTI value.

Is this true? How do you find out from the datasheet which method is used?

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Gain is absolutely the ONLY important part of PSRR. Essentially what you are saying is how much can an op-amp when feeding back a signal cancel out any ripples introduced from the power supply, not from the input of the circuit..

Lets take a simple example: an ideal (infinite open loop gain) voltage follower (output tied directly to the inverting input, fed from the non inverting input). The circuit has a closed loop gain of 1, but the feedback (since the overall gain is SOOO high) will mean that any power supply ripple will be canceled due to the feedback forcing the non inverting and inverting inputs to be in perfect lockstep..

But take the SAME example, but make the OPEN loop gain of the opamp 1, still with closed loop gain of 1, then suddenly the op amp can't keep up with the changes between the non-inverting input and the output-inverting input. And hence all ripple from the power supply would be visible on the output (essentially the op-amp would turn into a noise source with the noise being the coupled power supply ripple)

I understand HOW stevenvh could say that the gain is not meaningful, because he meant CLOSED loop gain... But the gain of question is OPEN loop gain, and YES, that is EVERYTHING in PSRR.

EDIT: And to answer your question, just to follow up slightly here, the PSRR is related to open loop gain, but the more closed loop gain you introduce, the more power supply ripple you will get on the output (hence the 60dB you reference above)

Here is why: Same example I give above, except this time you have a REAL op amp, (finite open loop gain), and resistors in your feedback path, meaning you have a closed loop gain of some value, say 6dB. Since the resistors behave as a voltage divider, the op-amp has to OVERCOMPENSATE for the power supply ripple being fed back to the non-inverting input. If it can only compensate for 100dB of power supply ripple, you will only get 94dB of rejection. The more closed loop gain you introduce, the less of the power supply ripple you are able to reject.

The whole conversation stems from the separate meanings of open loop and closed loop gain.

2nd EDIT: And the way that you get 60dB, or I get my 94dB is that you have to realize you have to convert dB BACK so for example you need to use

$$20 \log10\left(\frac{10^\frac{100}{20}}{10^\frac{6}{20}}\right) = 94 \mathrm{dB}$$

$$20 \log10\left(\frac{10^\frac{100}{20}}{10^\frac{40}{20}}\right) = 60 \mathrm{dB}.$$

And YES the other guy who said it should be 1mV not 1µV on Wikipedia is correct.

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The confusion here is that PSRR (Power Supply Rejection Ratio) is a general term which in practice is actually used to refer to multiple things. In general it is a ratio comparing a change in a parameter against a change in the supply's DC voltage level.

For example, PSRR in an ADC is often used to refer to the ratio of the Gain Error to Change in DC Voltage of the Supply.

Some of this comes from confusing the acronym PSRR, which can be used as:

"Power Supply Rejection Ratio" which is, as mentioned above, a ratio between a measured parameter and a change in the supply's DC voltage.

and

"Power Supply Ripple Rejection" which is the term which is, in general, the ratio of AC voltage on the supply to AC voltage on the input or output. But, this can also be a ratio of an input to an output in the case of something like an Linear Regulator.

Lets look at an example: http://focus.ti.com/lit/ds/symlink/opa121.pdf

Here you'll see in the table on page 2 a value listed under the "Offset Voltage" section as "Supply Rejection".

This is a "Power Supply Rejection Ratio" comparing changes in the supply's DC level to shifts in the output's offset voltage.

On page 3 a value listed under the "Input Offset Voltage" section as "Supply Rejection".

This is a "Power Supply Rejection Ratio" comparing changes in the supply level to shifts in the input offset voltage.

Looking at charts on page 4, we see a graph of "Power Supply Rejection vs Frequency".

This is a "Power Supply Ripple Rejection" measurement of AC ripple rejection which is the ratio of Supply Ripple to Input Ripple.

This last one may be a bit confusing as for an op-amp the "Power Supply Ripple Rejection" is often specified as a ratio of the supply ripple to the input ripple. This will generally be the case for devices with feedback or in the case of an op-amp, are generally used with feedback.

For devices without feedback, class D audio amplifiers for instance, "Power Supply Ripple Rejection" is usually just a ratio of the supply ripple to the output ripple and "Power Supply Rejection Ratio" is a measurement of the impact on the supply DC level to the output offset voltage.

In summary there isn't really a hard and fast definition for 'PSRR' and often other terms are used such as 'Supply Rejection', 'Ripple Rejection', 'Power Supply Rejection', etc. The important thing is that they are always measurements describing the effect of the power supply on the circuit in question. To figure out what the measurement really means you have to consider the context of the measurement as well as the mode of operation of the device.

EDIT: Here are some examples of different uses by manufacturer:

National Semiconductor: Uses the terms "Power Supply Rejection Ratio" for AC and "DC Power Supply Rejection Ratio" for DC.

Maxim: Uses "Power Supply Rejection Ratio" for DC and "Ripple Rejection" for AC

TI: Uses "Power Supply Ripple Rejection (PSRR)" LDOs and Various forms of "Supply Rejection" for Op-amps (see data sheet above).

Analog Devices: Uses "Power Supply Rejection Ratio" defines it as relating to either the input or output, and even argues that the term PSRR shouldn't be used if its expressed in dB but rather PSR (Power Supply Rejection) should.

There are many more examples but I'll leave it at that.

So again, there really is no standardized definition here, its all up to context.

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My question is about op-amps. I'm highly skeptical that there are distinct definitions for "Power Supply Rejection Ratio" (PSRR) and "Power Supply Ripple Rejection" (PSRR). I suspect they are the same thing, measured the same way, and the DC measurement is just the component at 0 Hz. The datasheets I'm looking at are by different manufacturers, and their charts are labeled "POWER-SUPPLY REJECTION RATIO vs. FREQUENCY" and "POWER SUPPLY REJECTION RATIO vs FREQUENCY". – endolith May 11 '11 at 18:48
@endolith I added several examples...there is no standardization in the industry when it comes to these terms, you just have to figure out what they are referring to by context or by looking at a particular manufacturers definitions. – Mark May 11 '11 at 19:22
Still looks like there's no difference between AC and DC measurements in op-amps, and the terms are used interchangeably. – endolith May 11 '11 at 19:49
@endolith the fact that there is no standard naming convention was indeed the point of my answer... – Mark May 11 '11 at 20:25

There is a PDF of op-amp test procedures on Intersil's website here which shows that PSRR is referred to the amplifier input. By my calculations, Wikipedia's 1uV output noise should read 1mV.

$20 \log(\frac{1\mathrm V}{1\mathrm{mV}/100})$ = 100dB

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Er, isn't 1 mV/100 not 10 uV? – stevenvh May 11 '11 at 15:59
@stevenvh 1mV output noise referred to the input of a X100 amplifier is 10uV and 20*log(1V/10uV) = 100dB – MikeJ-UK May 11 '11 at 16:02

Microchip's op-amp topologies paper explains it this way:

"In a closed-loop system, a less than ideal power supply rejection capability of an amplifier manifests itself as a offset voltage error..."

$PSRR(dB) = 20 log \frac {\Delta V_{SUPPLY}}{\Delta V_{OS}}$

$PSR(\frac{V}{V}) = \frac {\Delta V_{OS}}{\Delta V_{SUPPLY}}$

where

$V_{SUPPLY} = V_{DD} - V_{SS}$

$\Delta V_{OS} =$ input offset voltage change due to PSR

It also goes on to say that having bad PSR is not good for high-gain closed-loop amplifiers powered from batteries, as the DC change in supply voltage (as the battery discharges) will have a measurable affect on the output due to the input offset change.

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