# The Field Effect Transistor as a Voltage Controlled Resistor

An fet can be used as a voltage controlled resistor (vcr) where the resistance between the drain and source is controlled by the gate-source voltage. The resulting resistor is unfortunately non-linear; however, a simple linearisation circuit means that the fet vcr can be used even in situations where the non-linearities would cause difficulties. I have used this technique successfully both at audio and video frequencies. Typical applications include attenuators, amplifier and modulation circuits.

### Characteristics of a JFET

Consider the characteristics of a JFET with pinch-off voltage = VP :

There are two distinct regions - the saturation region (or pentode region) and the ohmic (or triode) region. In the saturation region the drain current is almost entirely independent of the drain-source voltage whilst in the ohmic region the drain current depends on the drain-source voltage.

The equation of the curve that separates the triode and pentode regions is:

| VDS |  =  | VP |  -  | VGS |

In the triode region:

 2IDSS ID » VDS(VGS - VP) - 0.5VDS2 (1) Vp2

 1 ID 2IDSS = » (VGS - VP) - 0.5VDS (2) rDS VDS VP2

If  VDS  =  0,  then for small signals about the origin:

 rds VP2 = VDS = 0 2IDSS (VGS - VP)

If   VDS   and  VGS  =  0,  then:

 rds 1 2IDSS VDS = 0 = = VGS = 0 rdso |VP|

In (2), we have a term: 0.5VDS  -  hence rds will vary with the voltage present across the transistor and the resistance will not be constant so we have a non-linear resistor.

This non-linearity can be removed by adding 0.5 VDS to VGS. This is achieved using the following circuit:

 R2 R1 VGS = VC + VDS R1+R2 R1+R2

Let: R1 = R2

thus: VGS = 0.5 (VC + VDS )

Substitute into (2):

 1 2IDSS = 0.5 (VC + VDS) - VP - 0.5VDS rDS VP2

Thus:

 1 2IDSS = 0.5 VC  - VP rDS VP2

Therefore: rDS is a linear resistor.

### Notes

1. Adding R1 and R2 reduces the control sensitivity by factor of two.
2. R1 + R2 should be high since R1 + R2 shunts rDS.
3. One terminal of the resistor must be at a fixed potential (e.g. the source must be grounded) or the control voltage must be allowed to float.
4. The control voltage should be supplied from a low impedance source (or R1 should be adjusted to compensate for the source impedance).

### Conclusions

The fet can be used as a voltage controlled resistor which can be used in audio applications. To ensure that distortion is minimised simple steps are taken to linearise the resistance. Applications include oscillators (where both frequency of operation and the feedback can be controlled), filters, modulators and automatic gain controls.

Last updated: 18 October 2002;   © Lawrence Mayes, 2001/02