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# I need some help with calculating input bias current, input offset voltage and PSRR

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#### Plecto

##### Full Member level 5
I would like to fill some holes in my op-amp knowledge. I currently have some static noise and slight humming in my recent amplifier design and I'm thinking that the source might be the PSRR of the op-amp used, but how do I calculate it? I made this simple circuit that has +/-25V rails with 1V of humming present:

First off, the input offset voltage is a voltage that is present on the input of the amplifier, right? This voltage will vary slightly with supply voltage so that any ripple present on the supply will appear on the inputs of the op-amp, is this correct? If the input bias voltage is equally present at both the inverting and non-inverting input of the op-amp won't they then always cancel each other out regardless of how much ripple that is present on the supply? Also, the input bias voltage has to depend on the input resistor as well, doesn't it? I've chosen a 100kOhm input resistor in this schematic, but as this value drops, so does the input bias voltage, doesn't it? I'm also wondering if perhaps the input bias current also varies with supply voltage? Thing is that the humming I have in my recently made real life amplifier will vary greatly with the input resistor value chosen, almost going completely away if I short the non-inverting input to ground.

The op-amp in the schematic attached is a OPA551 which has a 'input offset voltage vs. supply voltage' of 10uV/V. If I have 1V of ripple and a gain of 2.5, would that lead to an output voltage of 25uV? One last question about input bias current, how can current flow in or out of it's inputs when it's got fet inputs?

Look at the graph for the power supply rejection ratio versus frequency in the data sheet. It shows over 90dB rejection at 50Hz. That would give 31uV of noise with a 1V ripple on the power supply.

What value of output hum do you measure?

If the hum varies with input resistance, then I suspect you are picking up the hum from the air.
Is you input circuit shielded with shielded wires? You may need to run a shielded wire directly to the op amp input.

The amplifier has no input at all, I've removed the input caps.

The noise is hard to measure as I only have a Rigol DS1052E scope. I've made a small battery powered amp with a gain=100 in an attempt to be able to measure the noise, but I have to set the gain of the amplifier to 24 to actually be able to measure it. I'm getting something like 150mV of ripple noise, but it's hard to be exact. With a total gain of 2400 it would equate to about 60uV of noise begin present at the input which is not that far off from the 31uV you calculated? Also taking the upper harmonics of the ripple into account, the PSRR decreases at the frequency increases so at 400hz the PSRR is under 80dB which would clearly make 1V ripple audible. The thing I asked about in the opening post though, isn't the ripple present on both the + and - input thus canceling each other out?

...................The thing I asked about in the opening post though, isn't the ripple present on both the + and - input thus canceling each other out?
Depends upon the relative phase of the plus and minus ripple and whether the phase gets inverted in the internal circuitry of the op amp as compared to the input bias.
I don't think you can make any general rule about that and just assume worst-case (they add together).

Wikipedia says: "The input offset voltage (V_{os}) is a parameter defining the differential DC voltage required between the inputs of an amplifier, especially an operational amplifier (op-amp), to make the output zero (for voltage amplifiers, 0 volts with respect to ground or between differential outputs, depending on the output type)." which kind of answers my question. The input offset voltage is a differential voltage between the inputs, not with respect to ground (kind of obvious now that I think about it ).

I figured that the noise I'm hearing is not caused by too poor PSRR. 31*2.5=77uV at 100hz is not audible with this particular headset and the humming I'm hearing is clearly audible I did some measurements on a previous amplifier using the OPA454 instead of the OPA551. Even though the two has equal PSRR and equal ripple voltage, no hum is audible on the OPA454 amp even with a gain of 24 so I've clearly messed up something else.

I figured that the noise I'm hearing is not caused by too poor PSRR.
Yes, as crutschow stated, this has been alread proved by the shorted signal input test.

PSSR is describing the ratio of supply ripple to generated differential input voltage (similar to offset, as you stated), so there's no point of being cancelled out by the differential OP input.

Most hum injection in audio amplifiers is either capacitively or inductively coupled, it's usually easy to find the interference path by a number of tests.

So by shorting the input to ground I'm eliminating too poor PSRR as a possible source? Why is that?

It seems like the op-amp itself has to be part of the problem. Replacing the OPA551 with OPA454 decreased the hum to almost inaudibility. I have no idea what difference between the two op-amps that could do something like that

So by shorting the input to ground I'm eliminating too poor PSRR as a possible source?
The opposite is true. I confirmed your test result, showing that the interference source is not lack of PSSR respectively supply ripple. If it's PSSR, the hum would stay with shorted input.

Did you build the circuit on a solderless breadboard? Messy jumper wires and the many rows of contacts are antennas and pick up interference like mains hum. Replacing the opamp resulted in less hum maybe because the messy jumper wires were moved.

Did you build the circuit on a solderless breadboard? Messy jumper wires and the many rows of contacts are antennas and pick up interference like mains hum. Replacing the opamp resulted in less hum maybe because the messy jumper wires were moved.

The circuit is built on a pcb with all surface mount components.

The opposite is true. I confirmed your test result, showing that the interference source is not lack of PSSR respectively supply ripple. If it's PSSR, the hum would stay with shorted input.

So the hum is not because of poor PSRR nor is it coupled on the input as the input cap is removed so the input is only connected to a tiny strip of copper trace. One difference between the OPA551 and OPA454 is that the OPA551 has a higher quiescent current, enough to make the package rise to about 50C. This extra quiescent current will cause more current to flow from and to +V, -V and the op-amp. Perhaps the +V and -V rails couple to the input some how? Let's say the 0604 input cap of my amplifier runs directly over a trace, how much current has to travel through this trace for it to couple to the input cap above? Also, what about capacitive coupling between traces?

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With a gain of 22 the output looks like this:

What would cause a waveform like that?

The waveform looks like a copy of the current through a power supply filter capacitor. Either coupled by a ground loop or inductively.

Your problem is partially due to inductive coupling of current pulses on an AC bridge caps. If your inputs are not low impedance or perfectly balanced impedances on both inputs and cables and source connected to it, the mutual coupling of common mode H fields from current and E fields from voltage capacitively coupled to high impedance inputs, it will result in a differential input voltage.

If a low impedance common ground is not used, then any PS noise can couple by radiated noise in addition to conducted noise via Vcc, Vee.

If you short both inputs to 0V, you can measure CMRR.

If you have supply ripple in your unregulated or unfiltered supplies, with inputs grounded, it must be a conducted noise.

If you filter or regulate ripple, then it must be radiated noise from unshielded inputs with unbalanced transmission lines.

By the way (btw), SMPS are notorious for radiated CMRR with perfectly filtered DC , with low DM(differential mode) noise, due to high CM noise and lack of CM ferrite LC filtering.

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Also btw, if you balance Req on each input, then Vio due to Iin will be balanced for DC too.

Single ended inputs require excellent shielding and low radiated noise current pulses.

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