Demand for voltage-controlled current sources (VCCSs) and multipliers in a wide spectrum of electronics and communication devices always seems to exist. The multipliers employed in circuits like the Gilbert Cell, however, produce outputs proportional to the product of two voltages. Research, as well as commercial applications, perpetually confronts the problem of implementing a single-ended multiplier with an output that's produced from the differences of two pairs of voltages. The circuit that's described below offers a simple and inexpensive solution.

To realize a differential VCCS (DVCCS), one must consider its design elements,
which can be traced from the linear voltage-controlled resistor (VCR). The simplified
circuit in Figure 1 shows a linear VCR, whose
value can be either positive or negative depending on V_{G1} and V_{G2}
applied to the gates of the MOSFETs. Assuming identical MOSFETs, the equivalent
resistance (R_{EQ}) at the input (V1) is:

R_{EQ} = V_{1}/i_{1} = \[K(V_{G1}-V_{G2})\]^{-1}
(1)

where K = µsCOX(W/L). W/L is the aspect ratio, µs is the electron
mobility, and COX is the gate oxide capacitance. These results were obtained
using the I_{D}-V_{DS} relationship in the triode region.

Equation 1 shows the equivalent resistance as the difference of two voltages. This can be exploited to implement a DVCCS. By ungrounding the two MOSFETs and interchanging M2 and CCII(+), and by making small modifications/additions, we obtain a new circuit—a DVCCS, or a two-quadrant multiplier.

Figure 2 shows the circuit realized as suggested above in design basics. The circuit consists of two MOSFETs and two current conveyors: CCII(+) and CCI(-). The currents iD1 and iD2 in the triode operating region of the MOSFET are:

i_{D1} = K \[(V_{4}− V_{2}− V_{TH})− ((V_{1}− V_{2})/2)\](V_{1}− V_{2}) (2)

i_{D2} = K \[(V_{3}− V_{2}− V_{TH})− ((V_{1}− V_{2})/2)\](V_{1}− V_{2}) (3)

Also, the currents i2 and i0 (assuming an ideal current conveyor; that is, I_{X} = I_{Z}, I_{X} = I_{Y}, V_{X} = V_{Y}, for CCI(+), and I_{X} = −I_{Z}, I_{X} = I_{Y}, V_{X} = VY, for CCI(−)) are:

i_{2} = i_{D2}− i_{D1} (4)

i_{0} = −i_{2} (5)

Performing a complete mathematical analysis using Equations 2 through 5, we get the current at the output terminal as:

i_{0}= K\[(V_{1}−V_{2})(V_{3} −V_{4})\] (6)

Any three of the four voltages may be kept constant, and current may be obtained in proportion to the fourth one. Consequently, a conventional VCCS is realized. If all four voltages are varying, we obtain a differential VCCS. That is, the output current is proportional to the difference of two voltages and another two voltages.

Moreover, the DVCCS also can be visualized as a two-quadrant multiplier where the product of two voltages yields a proportionate current. Because V3 and V4 are applied to the gate terminals of the MOSFETs, they must always be positive. Furthermore, the direction of the current may be controlled by varying different voltages.

The circuit makes the most out of the MOSFET's beneficial characteristics—low power consumption, high input impedance, low fabrication cost by increasing cell density—with complete elimination of nonlinear square properties. As a result, the DVCCS rightly falls into the category of externally linear, internally nonlinear (ELIN) circuits.

Figure 2 shows how all voltages see a high input impedance. Also, with the current available at the Z terminal of the current conveyor, the current output is available from a low impedance source. This clearly shows that the realized VCCS is similar in characteristics to an ideal VCCS.

This circuit was simulated using Electronics Workbench (MultiSim). Its characteristics were verified using PSpice, which confirmed the expected voltage-current linearity.

To the author's best knowledge, no commercially available IC performs conversion of a differential voltage to a single-ended current. Implemented as an IC, this circuit would require only seven terminals: four voltage inputs, one current output, and two power-supply terminals.

The differential VCCS may find applications in AGC amplifiers, amplitude modulators, double-sideband modulators and detectors, single-sideband modulators and detectors, AM detectors, frequency doublers, squaring circuits, dividers, square-root circuits, rms measuring circuits, microemissive displays, temperature controllers, remote error sensors, and so on.

Acknowledgments: The author pays special thanks to Professor Raj Senani, Analog Signal Processing Research Lab., Netaji Subhas Institute of Technology (NSIT), New Delhi, India, for providing valuable suggestions in the classroom.