I have seen quite a few schematics lately that are using an operational amplifier (opamp) configured as a negative resistor. I thought it would be interesting to analyze this circuit and show how it can provide an economical solution to a common sensor interface scenario.
Figure 1 illustrates a common sensor interface scenario. This scenario consists of:
The sensor has a resistance characteristic that varies according to some external parameter, e.g. temperature, ambient light level, gas concentration.
- Current Source
A current source drive can be desirable for a number of reasons: (1) The sensor may be calibrated for a specific current level, (2) The sensor may have a linear response for a given current drive, (3) The sensor output voltage range needs to be restricted in some way.
The amplifier is often needed to provide isolation from the monitoring circuitry and to scale the output for further signal processing.
Negative Resistance Opamp Circuit
Figure 2 shows an operational amplifier connected as a negative resistance.
Equation 1 shows the derivation of the negative resistance equation.
Equation 2 shows the derivation of the voltage gain equation.
My application example is shown in Figure 4.
The basic idea here is to use negative input resistance of the opamp circuit to cancel out the resistance of RS. Figure 4 illustrates this source transformation.
The parameters of this case are the following:
Figure 4 shows my solution in Mathcad.
I worked through some basic design equations for the application of a negative resistance circuit to a sensor interface example. I have been seeing this circuit quite a bit lately and it is an interesting application of basic linear circuit analysis.