# Voltage-to-Current converter offers precisely defined dead-band

In the control of nonlinear *and* linear systems, sometimes a slight nonlinearity is intentionally inserted into the closed control loop. “Slight” here means that the output of the inserted element starts to vary linearly, but only once the input exceeds a nonzero threshold value. For inputs from zero to the threshold, the output of the element has zero value. The result is that adding of this nonlinear element can quench damped oscillations, which are typical for feedback systems.

The unipolar voltage-to-current converter in Fig. 1 is based on a classical connection of op-amp IC2a and NPN transistor Q1. The regulated current flows through emitter resistor R_{E}, which acts here as a simple passive current-to-voltage converter. In the closed-loop, actual negative feedback is the voltage fed to the inverting input of IC2a. A dead-band in the V-I characteristic is created by current flowing from the source of reference voltage, V_{REF}, through resistors R_{D}, R_{E} to ground. The reference voltage V_{REF} is derived from the band-gap cell IC1, resistive divider R_{a}, R_{b, }and op amp IC2b.

**Figure**** 1** Output current of the converter rises linearly for input voltage rising within the range of 20mV to 200mV, while it has zero value for V_{IN} below 20mV.

To evaluate this dead-band quantitatively, you can firstly assume V_{IN} equal to zero. The op-amp tries to force V_{ED} to zero as well. This however is not possible, as the B-E junction of Q1 acts now as a reverse-biased diode. The result is that the emitter current of Q1 is zero, and consequently the voltage-drop at resistor R_{E}, is:

(1)

As the same voltage appears at inverting input of the op amp, its output is saturated at zero-level.

When you start to elevate the level of V_{IN} from zero value, the situation remains steady until V_{IN} value exceeds that of V_{ED}, given by Equation 1. At that instant the output voltage of op-amp IC2a becomes positive, causing a current
to flow through the emitter of Q1. The higher the value of V_{IN} is, the higher is the emitter current of Q1. Due to a strong negative feedback, the dependence I(V_{IN}) is linear for V_{IN} within the V_{ED} to V_{REF} range. To evaluate the output current at full-scale input voltage, V_{IN} = V_{REF}, you can realize that the R_{D} resistor has the same voltage, V_{REF}, at both its ends, so no current flows through it. The equivalent emitter resistor at the full-scale output current is therefore R_{E} itself, and the value of emitter full-scale current is V_{REF}/ R_{E}.

The output current flowing across the collector of Q1 and positive supply terminal, is very close to emitter current:

where

*β*is the current gain of Q1. The V-I characteristic of the converter is drawn in Fig. 2.

**Figure 2**

For the 2N3904 transistor, *β* ≈ 230; thus the collector current is about 0.44% lower than its emitter current. To lower this error, you could use a Darlington pair, or a cascade of two bipolar transistors, in place of Q1. The input voltage, V_{IN}, can be derived either from potentiometer P1 or an external source.

If you choose, for example V_{DB} = 0.1×V_{REF}, V_{DB} = V_{ED} you get from Equation 1 that R_{D} = 9R_{E}. A theoretical dependence of output current on input voltage is depicted in Fig. 2.

Experimentally, V_{REF} = 0.19645V and full-scale emitter voltage V_{ED} = 0.19660V have been measured. The V_{DB} has been determined by detecting an abrupt change at the output of IC2a of either zero-to-positive, or positive-to-zero voltage transitions, and by measuring the V_{IN} value at this instant. V_{DB} = 19.75mV for positive transitions and V_{DB} = 19.70mV for negative transition have been measured.

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