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**Input Offset Voltage Drift and Aging Effects**
When the bias currents of an op amp are well matched (the case with simple bipolar op amps, but not internally bias compensated ones, as noted previously), a bias compensation resistor, R3, (R3=R1||R2) introduces a voltage drop in the non-inverting input to match and thus compensate the drop in the parallel combination of R1 and R2 in the inverting input. This minimizes additional offset voltage error, as in Figure 1-46.

Figure 1-46: Canceling the effects of input bias current within an application

Note that if R3 is more than 1kΩ or so, it should be bypassed with a capacitor to prevent noise pickup. Also note that this form of bias cancellation is useless where bias currents are not well-matched, and will, in fact, make matters worse.

**Calculating Total Output Offset Error Due to I**

_{B}and V_{OS}
The equations shown in Figure 1-47 below are useful in referring all the offset voltage and induced offset voltage from bias current errors to the either the input (RTI) or the output (RTO) of the op amp. The choice of RTI or RTO is a matter of preference.

Figure 1-47: Op amp total offset voltage model

The RTI value is useful in comparing the cumulative op amp offset error to the input signal. The RTO value is more useful if the op amp drives additional circuitry, to compare the net errors with that of the next stage.

In any case, the RTO value is simply obtained by multiplying the RTI value by the stage noise gain, which is 1 + R2/R1.

Before departing the topic of offset errors, some simple rules towards minimization might bear repetition:

- Keep input/feedback resistance values low, to minimize offset voltage due to bias current effects.
- Use a bias compensation resistance with VFB op amps not using internal bias compensation. Bypass this resistance, for lowest noise pickup.
- If a VFB op amp does use internal bias current compensation, don't use the compensation resistance.
- When necessary, use external offset trim networks, for lowest induced drift.
- Select an appropriate precision op amp specified for low offset and drift, as opposed to trimming.
- For high performance, low drift circuitry, watch out for thermocouple effects and used balanced, low thermal error layouts.

**Input Impedance**

VFB op amps normally have both differential and common-mode input impedances specified. Current feedback op amps normally specify the impedance to ground at each input. Different models may be used for different voltage feedback op amps, but in the absence of other information, it is usually safe to use the model in Figure 1-48 below. In this model the bias currents flow into the inputs from infinite impedance current sources.

Figure 1-48: Input impedance (voltage feedback op amp)

The common-mode input impedance data sheet specification (Z

_{cm+}and Z_{cm–}) is the impedance from either input to ground (NOT from both to ground). The differential input impedance (Z_{diff}) is the impedance between the two inputs. These impedances are usually resistive and high (10^{5}-10^{12}Ω) with some shunt capacitance (generally a few pF, sometimes 20-25 pF). In most op amp circuits, the inverting input impedance is reduced to a very low value by negative feedback, and only Z_{cm+}and Z_{diff}are of importance.
Figure 1-49: Input impedance (current feedback op amp)

A current feedback op amp is even more simple, as shown in Figure 1-49 above. Z+ is resistive, generally with some shunt capacitance, and high (10

^{5}-10^{9}Ω) while Z– is reactive (L or C, depending on the device) but has a resistive component of 10-100Ω, varying from type to type.
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