TABLE OF CONTENTS Squaring and square-rooting are basic functions in the amplitude domain, the need for which arises quite often. They are essential to the extraction of the exact RMS value of a signal, and in power measurement in general. It is possible to devise TN circuits, involving voltage-in current-out signals, to approximate the squaring function in two quadrants (that is, the output is of the same sign for either input). Figure 2.10 shows a circuit which provides an effective solution for input voltages Vin of up to 150mV peak; larger inputs are accommodated by simply adding a resistor in series with the input. The use of the resistor divider formed by the two base resistors, R, results in one of the two outer transistors to conduct more heavily whether Vin swings either positive or negative. The form of the resulting collector currents is approximately a hyperbolic cosine. The output amplitude can be shown to be maximal (49.23% of the tail current Ie) when the area ratio A=6. However, the function accuracy at this input level is improved using A=10, when the output amplitude is still about 47% of Ie. The standing current in Q2 for Vin=0 is withdrawn by the collector bias current Ic. Using Ie=1.06mA and Ic=880 ?A, the output is zero for Vin=0 and 500 ?A for Vin= 150mV. The load circuit would preferably be set about a V BE above ground, but because of the small voltage swings all collectors can be grounded.
