# Measuring amplifier DC offset voltage, PSRR, CMRR, and open-loop gain

-February 19, 2014

Operational amplifier (op amp) offset voltage is an important parameter to understand. It is a voltage error that is a consequence of the op amp’s mismatched input amplifier stage (Figure 1).

Figure 1 Diagram of a typical operational amplifier showing position of offset voltage (VOS) error.

The offset error appears as a DC voltage at the output pin (VOUT, Figure 2). The offset-voltage (VOS) is gained by two from the relationship, G = (1 + R2 / R1); This is the same as a voltage source connected to the amplifier’s non-inverting input (IN+) of your amplifier. If you have a high closed-loop gain around the amplifier, the offset voltage appears as a significant voltage error in any precision circuit that you may implement.

Figure 2 Amplifier application circuit to measure DC VOS, PSRR, CMRR, and AOL.

But, the consequence of this error goes much deeper than simply an output offset voltage. Its level may shift the results of some of the amplifier’s other important parameters: the power-supply-rejection-ratio (PSRR), the amplifier’s common-mode-rejection-ratio (CMRR), and the open-loop-gain (AOL) specifications.

You can measure the PSRR by changing the power supply voltages and how the voltage offset changes. The amplifier CMRR is measured by observing how the voltage offset changes as the input common-mode voltage at the amplifier’s input stage changes. Finally, AOL is measured by observing VOS changes as VOUT changes.

Figure 2 shows a simple circuit diagram that you can use when measuring these specifications at DC. In this circuit, VOS is extracted at the VX node. From the VX value you can calculate the offset voltage (VOS). It is equal to, VOS = VX*R4/(R3+R4).

For the PSRR specification the applicable formula is:

Where PSRR is equal to the power-supply-rejection-ratio specified in dB,
VP is the positive voltage supply
VN is the negative voltage supply
VOS is the measured operational amplifier offset voltage

Referring to Figure 2, one measures VOS for two power supply settings. As you change the power supply voltages, be careful to stay within the amplifier’s operating specifications. During this test, the input common-mode-voltage (CMV), or V1, and the amplifier’s VOUT remain set to the mid-supply level. If the output does not remain at that level, you can manipulate this voltage by adjusting V2.

Similar techniques are used to measure the CMRR of an amplifier. Changing the input CMV (V1) causes VOS to change. The formula for CMRR is:

Where CMRR is equal to the common-mode-rejection-ratio in db:
V1-1 is the first common-mode voltage setting
V1-2 is the second common-mode voltage setting
VOS is the measured operational amplifier offset voltage

Again, it is important to make sure that the output voltage remains halfway between the two power supply voltages. This can be accomplished by adjusting V2. Also, the power supplies remain constant. Additionally, be careful to keep the non-inverting input pin (V1) within the product data sheet’s limits.

The final DC test is open-loop-gain (AOL). AOL is equal to changes in the output voltage with respect to changes in the offset voltage. You can change the output voltage by changing the voltage at the V2 node in Figure 2. The formula for AOL is:

Where AOL is equal to the amplifier’s open-loop-gain in dB:
VOUT is the output voltage of the amplifier
VOS is the measured operational amplifier offset voltage

In this case, it is important to make sure that the input common-mode voltage (V1) remains halfway between the power supply voltages, and that the power supplies are constant. Additionally, during this measurement the output voltage pin (VOUT) must remain within the product data sheet’s specified limits.

Table 1 summarizes all of these test conditions.

Table 1 VOS, PSRR, CMRR, and AOL test guidance for Figure 1 circuit.

You can change the voltage of V2 to meet the conditions in Table 1.

These are easy DC tests to run when you are trying to understand how the amplifier reacts to the different power supply, common-mode input voltage, and output voltage conditions. Give these tests a try on your favorite amplifier and compare your results to the respective product data sheet. I would like to know if you get your expected results.

References
1. What you need to know about CMRR – the operational amplifier (Part 1),” Matthew Pickett, Analog Wire, Texas Instruments
2. Will the real Vos please stand up?,” Tim Green, Precision Designs Hub, Texas Instruments
3. My amplifier has high PSRR, so I don’t need to worry about supply variation…Right?,” Art Kay, Precision Designs Hub, Texas Instruments
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