Below are excerpts from technical documents of two different general-purpose op-amps as examples.
To investigate the effect of Ios, Vos, and Ib parameters indicated in the technical documents on the op-amp output, a sample op-amp circuit with negative feedback is provided below.
Bias Current & Offset Current (exc: Opamp Offset Voltage)
To only observe the effect of bias currents in the sample feedback op-amp circuit in Figure 2, the input voltage is changed to 0V. By showing the input bias currents on the circuit diagram, the schema in Figure 3(A) is obtained.
The terms IB+ and IB− and their equivalents for the "Input Bias Current" and "Input Offset Current" parameters mentioned in the technical documents are represented in equations eq.1 and eq.2.
In the obtained circuit diagram, the IB+ current will not cause a voltage difference at the op-amp input. In this case, the voltage at the V- point will be 0V, and since no current will pass through the R1 resistor, all of the IB- current will pass through the RF resistor. The simplified version of the sample circuit is shown in Figure 3(B).
The voltage observed at the output of the opamp in Figure 3(B) will be represented by the equation eq.3.
If an RC compensation resistor is added to the sample feedback op-amp circuit, the schema in Figure 4 is obtained.
In the feedback op-amp circuit in Figure 4, to only observe the effect of bias currents, the input voltage is changed to 0V. By showing the input bias currents on the circuit diagram, the schema in Figure 5 is obtained.
In order to calculate the voltage to be seen at the opamp output in the diagram in Figure 5, the effect of each of the IB+ and IB- current sources on the opamp output is calculated separately.
From the circuit diagram in Figure 6 (A), (eq.4) and (eq.5) are obtained.
From the circuit diagram in Figure 6 (B), (eq.6) and (eq.7) are obtained.
If the equations for the circuit diagram in Figure 5 are summed up, the result (eq.9) is reached by considering (eq.8).
In order to better see the effect of the RC resistor, the (eq.10) and (eq.11) equations have been adjusted.
At this point, if the RC resistance is equal to the parallel sum of the R1 and RF resistors as shown in the equation (eq.12), the equation (eq.14) is reached.
When we use the (eq.2) equation in the (eq.14) equation, we finally get the (eq.15) equation.
Consequently, the RC compensation resistor is implemented in circuit diagrams with the intent of maintaining lower voltage discrepancies at the output, especially in opamps where the "Input Bias Current" value significantly surpasses the "Input Offset Current" value. Most of the time, the RC resistor is selected to match the parallel summation of the R1 and RF resistors.
Opamp Offset Voltage
To analyze the influence of bias currents and offset voltage on the output of the opamp within the example negative feedback opamp configuration depicted in Figure 4, the input voltage was adjusted to 0V. Figure 7 presents the derived diagram, showcasing both the input bias currents and the offset voltage on the circuit schematic.
The equation (eq.16) is obtained from the circuit diagram in Figure 8.
If the equations for the circuit diagram in Figure 7 are summed up (eq.17), the result (eq.18) is reached.
If the RC resistor is set equal to the parallel combination of the R1 and RF resistors, as indicated in equation eq.12, and by following analogous steps, then for the opamp circuit in Figure 4 with an input voltage of 0V, the equation eq.19 represents the total offset voltage observed at the output.