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MOSFET-based, analogue circuit computes square root

25 Jan 2016  | Abhirup Lahiri

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Square-root-calculating circuits are widely used in instrumentation and measurement systems for such tasks as calculating the root-mean-square (rms) value of an arbitrary waveform, for example. Hence, designers need an effective analogue square-root calculator. Because manufacturers do much of the IC fabrication in MOS technology, a MOSFET-based, analogue square-root calculator seems appropriate. This design idea describes such a circuit, which uses only MOSFETs to provide the square-root function (figure). The design is simple and versatile and can provide the output as the square root of the difference of two voltages.

Figure: This circuit uses only MOSFETs to provide the square-rooting function.

The circuit uses the nested connection of MOSFETs Q1 and Q2. Q2 works in the saturation region as it is diode-connected, forcing Q1 to work in the triode region. All other MOSFETs work in the triode region. The first part of the circuit, comprising Q3, Q4, Q5, and Q6, creating the current IO1, is basically a MOS-resistive circuit. The essential equation governing the circuit operation is:

where K1 and K2 represent the aspect ratios of transistors Q1 and Q2, respectively: KI=(µCOXW)/2LI, where I=K1=K2. The MOSFETs creating the MOS-resistive circuit and hence responsible for the current creation are identical, having the same aspect ratio and threshold voltage. The current relates to inputs V1 and V2, as the following equation shows: IO1=G(V1−V2), where G=2K(VA−VB) and represents the conductance of the MOS-resistive circuit—k=(µCOXW)/2L—of the identical transistors forming the MOS-resistive circuit, and VA and VB are control voltages applied to the gate of the MOSFETs that are working in the triode. This approach provides the advantage of voltage controllability of the output; hence, the square-rooting function is voltage-controllable.

The following equation gives the output voltage:

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