Opamp Input Bias Current, Offset Current and Offset Voltage

Error sources in opamp circuits are not limited to gain, bandwidth, or supply voltage. Especially in precision measurement, low-level signal processing, and high-impedance circuits, parameters such as input bias current, input offset current, and input offset voltage can cause significant output voltage shifts.

In this article, the effects of the Input Bias Current, Input Offset Current, and Input Offset Voltage parameters, which are specified in opamp datasheets, are examined through a sample negative-feedback opamp circuit.

Figure 1: Datasheet excerpts for (A) AD8538 and (B) LM747 opamps.

A sample negative-feedback opamp circuit is used to examine how the Ios, Vos, and Ib parameters specified in datasheets affect the opamp output.

Figure 2: Sample opamp circuit with negative feedback.

Opamp Input Bias Current and Offset Current

In the negative-feedback opamp circuit shown in Figure 2, the input voltage is assumed to be 0 V in order to examine only the effect of the input bias currents. When the input bias currents are shown on the circuit diagram, the equivalent circuit in Figure 3(A) is obtained.

Figure 3: (A) Equivalent circuit obtained when the input voltage is selected as 0 V and the input bias currents are shown on the circuit. (B) Simplified equivalent circuit.

The relationship between the Input Bias Current and Input Offset Current parameters given in datasheets and the opamp input currents IB+ and IB− is shown in Equation 1 and Equation 2.

Equations defining input bias current and input offset current using IB plus and IB minus.

In this circuit, the IB+ current does not create a voltage difference between the opamp inputs. Therefore, the voltage at the non-inverting input is considered to be 0 V. Due to the virtual ground effect, the voltage at the inverting input also remains at 0 V. In this case, no current flows through the R1 resistor, and the entire IB− current flows through the RF feedback resistor.

The simplified circuit for this condition is shown in Figure 3(B). In the circuit shown in Figure 3(B), the voltage shift observed at the opamp output is expressed by Equation 3.

Equation showing the output voltage shift caused by IB minus flowing through the feedback resistor RF.

This result shows that the input bias current can create a non-negligible DC error at the output, especially in circuits that use large feedback resistor values.

Effect of the Compensation Resistor

To reduce the output shift caused by the input bias current, a compensation resistor can be added to the non-inverting input of the opamp. When the RC compensation resistor is added to the sample circuit in Figure 2, the circuit shown in Figure 4 is obtained.

Figure 4: Circuit diagram obtained by adding the RC compensation resistor.

In this circuit, the input voltage is again assumed to be 0 V in order to examine only the effect of the bias currents. When the input bias currents are shown on the circuit, the equivalent circuit in Figure 5 is obtained.

Figure 5: Equivalent circuit obtained when the input voltage is selected as 0 V and the input bias currents are shown on the circuit.

To calculate the total voltage at the opamp output in the circuit shown in Figure 5, the effects of the IB+ and IB− current sources on the output are examined separately.

Figure 6: (A) Case where only the IB+ current source is active. (B) Case where only the IB− current source is active.

From the circuit shown in Figure 6(A), Equation 4 and Equation 5 are obtained.

Equations showing the voltage at the non-inverting input and the output contribution caused by IB plus.

From the circuit shown in Figure 6(B), Equation 6 and Equation 7 are obtained.

Equations showing the output contribution caused by IB minus through the feedback resistor RF.

For the circuit shown in Figure 5, the total output voltage is expressed as the sum of these two effects, as shown in Equation 8. When these expressions are combined, Equation 9 is obtained.

Equations combining the IB plus and IB minus effects to calculate the total output voltage shift.

Equation 9 can be rearranged to show the effect of the RC compensation resistor more clearly. As a result of this rearrangement, Equation 10 and Equation 11 are obtained.

Rearranged equations showing the effect of the compensation resistor RC on the total output voltage shift.

At this point, if the RC resistor is selected to be equal to the parallel equivalent of R1 and RF, as shown in Equation 12, Equation 13 and Equation 14 are obtained.

Equations showing that selecting RC equal to R1 in parallel with RF reduces the output shift to the input offset current term.

When the Input Offset Current definition given in Equation 2 is used in Equation 14, the total output voltage shift is expressed by Equation 15.

Total output voltage shift expressed using input offset current IOS and feedback resistor RF.

As a result, the RC compensation resistor is used to reduce the output voltage shift in opamps where the input bias current is much larger than the input offset current. Therefore, the RC resistor is usually selected to be close to the parallel equivalent of R1 and RF.

Effect of Offset Voltage on the Output

In the negative-feedback opamp circuit with a compensation resistor shown in Figure 4, the effects of both the input bias currents and the input offset voltage on the output are examined. For this purpose, the input voltage is again assumed to be 0 V. When the input bias currents and the input offset voltage are shown on the circuit, the equivalent circuit in Figure 7 is obtained.

Figure 7: Equivalent circuit obtained when the input voltage is selected as 0 V and the input bias currents and offset voltage are shown on the circuit.

To calculate the total voltage at the opamp output in the circuit shown in Figure 7, the effects of the IB+, IB− current sources and the VOS voltage source are evaluated separately. Therefore, in addition to the cases shown in Figure 6(A) and Figure 6(B), the case shown in Figure 8 must also be considered.

Figure 8: Case where only the VOS voltage source is active.

From the circuit shown in Figure 8, Equation 16 is obtained.

Equation showing the output contribution caused by input offset voltage VOS and closed-loop gain.

For the circuit shown in Figure 7, the total output voltage is written as shown in Equation 17. When these expressions are combined, Equation 18 is obtained.

Equations combining bias current and input offset voltage effects to calculate the total output voltage shift.

If the RC resistor is selected to be equal to the parallel equivalent of R1 and RF, as shown in Equation 12, the total output shift can be expressed by Equation 19 by following the same steps used in the previous section.

Final equation for total output voltage shift caused by input offset voltage and input offset current.

This equation shows that when a compensation resistor is used, the effect of the input bias current can be significantly reduced. However, the input offset voltage continues to appear at the output after being multiplied by the closed-loop gain of the circuit.

Conclusion

In opamp circuits, input bias current, input offset current, and input offset voltage are important error sources, especially in precision DC measurement applications. In circuits where large feedback resistor values are used, the output shift caused by bias currents becomes more significant.

A compensation resistor added to the non-inverting input is an effective method for reducing the error caused by input bias currents. This resistor is usually selected to be close to the parallel equivalent of the input resistor and the feedback resistor. In this way, the output error is mainly determined by the input offset current and the input offset voltage.

Therefore, in precision opamp circuit design, not only gain and bandwidth but also Input Bias Current, Input Offset Current, and Input Offset Voltage parameters should be carefully evaluated.