Simulation of a transconductance multiplier circuit has been covered previously. We now look at experimental multiplier behavior.

The circuit simulated previously is shown in implemented form below.

In this test circuit, divider voltage V_D (VD) is a variable supply, used to set the input diode current. It corresponds to Vs2 of the simulation. The 5 kHz source, v_M (vM) is a HP3314A function generator set to a 1 V pk-pk sinusoid with a frequency of 5 kHz. The variable voltage source in the circuit supplies a dc v_I corresponding to Vs1 of the simulation. All resistors are of ±1 % tolerance except the 2.2kW.

The output voltage, v_O, magnitude due to v_M is measured as peak-peak values and plotted below against dc values of v_I and V_D.

The S-shaped curve for positive v_I (v_IN graph label) at low V_D and the (inverted) bow for negative values shows the linearity limitations of the circuit. Linearity improves with larger divisor values. Note also the asymmetry of the output.

The plot of output voltage against input for dc (average) values, measured with a Keithley 2000 multimeter, has somewhat better linearity. The asymmetry around zero input remains due to the bowing of the curve. If a line is drawn tangent at the origin to the (red) curve, the positive and negative inputs correspond to about the same absolute values. For instance, at ±2 V for v_I , the output is about ±700 mV for V_D = 5 V.

The bow in the curve is due partly to emitter resistance in the gain-cell transistors. Resistance in series with a pn junction contributes an exponential nonlinearity that bows the curves. This circuit also uses voltage sources instead of current sources for inputs. The sources have 100 kW series resistance, which, being less than infinity, also introduce an exponential component to the curve. The simulation plot shows the same bowing effect for the simulated circuit.

The gain-cell multiplier/divider is neither complex nor expensive for applications such as power-factor corrector current-loop variable-gain amplifiers. Existing low-cost ICs require few additional parts to multiply and divide.

Ó Dennis L. Feucht, 2000