# 5.6: Drift

Drift is a variation in the output offset voltage. Often, it is temperature induced. Even if a circuit has been manually nulled, an output offset can be produced if the temperature changes. This is because $$V_{OS}$$ and $$I_{OS}$$ are temperature sensitive. The only way around this is to keep the circuit in a constant temperature environment. This can be very costly. If the drift can be kept within an acceptable range, the added cost of cooling and heating equipment may be removed. As you might expect, the magnitude of the drift depends on the size of the temperature change. It also depends on the $$I_{OS}$$ and $$V_{OS}$$ sensitivities. These items are $$\Delta V_{OS}/\Delta T$$, the change in $$V_{OS}$$ with respect to temperature, and $$\Delta I_{OS}/\Delta T$$, the change in $$I_{OS}$$ with respect to temperature. Drift rates are specified in terms of change per centigrade degree. These parameters are usually specified as worst-case values and can produce either a positive or negative potential.

The development of the drift Equation pretty much follows that of the Equation for offsets. The only difference is that offset parameters are replaced by their temperature coefficients and the temperature change. The products of the coefficients and the change in temperature produce an input offset voltage and current.

$V_{drift} = \frac{\Delta V_{OS}}{\Delta T} \Delta T A_{noise} + \frac{\Delta I_{OS}}{\Delta T} \Delta T R_f \label{5.21}\tag{5.21}$

As with the offset calculation, the drift result may be either positive or negative. Also, because $$I_{OS}$$ is so small for FET input devices, $$\Delta I_{OS}/\Delta T$$ is often not listed, as it is almost always small enough to ignore. For lowest drift, it is assumed that the op amp uses the offset compensation resistor $$R_{off}$$, and that the circuit has been nulled.

Example $$\PageIndex{1}$$

Determine the output drift for the circuit of Figure 5.5.3 for a target temperature of 80$$^{\circ}$$C. Assume that $$R_{off} = 909 \Omega$$ and that the circuit has been nulled at 25$$^{\circ}$$C.

The parameters for the 5534 are $$\Delta V_{OS}/\Delta T = 5 \mu V/C^{\circ}$$, $$\Delta I_{OS}/\Delta T = 200 pA/C^{\circ}$$.

The noise gain was already determined to be 11 in Example 5.5.1. The total temperature change is from 25$$^{\circ}$$C to 80$$^{\circ}$$C, or 55C$$^{\circ}$$.

$V_{drift} = \frac{\Delta V_{OS}}{\Delta T} \Delta T A_{noise} + \frac{\Delta I_{OS}}{\Delta T} \Delta T R_f \notag$

$V_{drift} = 5 \mu V/C^{\circ}\times 55C^{\circ}\times 11+200 pA/C^{\circ}\times 55C^{\circ}\times 10 k \notag$

$V_{drift} = 3.025mV+.11mV \notag$

$V_{drift} = 3.135mV \notag$

Note that for this circuit the $$V_{OS}$$ drift is the major source of error. At 80$$^{\circ}$$C, the output of the circuit may have up to $$\pm$$3.135 mV of DC error.

As with offsets, drift is partially a function of the circuit gain. Therefore high gain circuits often appear to have excessive drift. In order to compare different amplifiers, input referred drift is often used. To find input referred drift, just divide the output drift by the signal gain of the amplifier. Don't use the noise gain! In this way, both inverting and noninverting amplifiers can be compared on an equal footing. For the circuit just examined, the input referred drift is

$V_{drift (input)} = \frac{V_{drift}}{A_v} \notag$

$V_{drift (input)} = \frac{3.135 mV}{11} \notag$

$V_{drift (input)} = 285 \mu V \notag$

For many applications, particularly those primarily concerned with AC performance, drift specification is not very important. A communications amplifier, for example, might use an output coupling capacitor to block any drift or offset from reaching the output if it had to. Drift is usually important for applications involving DC or very low frequencies where coupling capacitors are not practical.