*D Ramírez, S Casans, C Reig, AE Navarro, and J Sánchez*

*EDN*

Although well-known to active-filter theorists and designers, GICs (generalized impedance converters) may be less familiar to analog generalists. Comprising a one-port active circuit typically comprising low-cost operational amplifiers, resistors, and capacitors, a GIC transforms capacitive reactance into inductive reactance and thus can substitute for an inductor in a filter that an RLC-transfer function describes. In addition, the flexibility of a GIC's input-impedance equation permits the design of virtual impedances that don't exist as physical components – for example, frequency-dependent resistance (Reference 1). The GIC, which its developers introduced 30 years ago, has seen its greatest application in ac-circuit and active-filter applications.

Figure 1. |
A classic generalized impedance converter provides a single-portimpedance that appears at V _{IN}. The schematic omits powerconnections for clarity. |

Figure 1 shows a classic GIC circuit in which the input impedance, ZIN, depends on the nature of impedances Z_{1} through Z_{5}. The following equation describes the circuit's input impedance:

For example, if Z_{1}, Z_{2}, Z_{3}, and Z_{5} comprise resistors R_{1}, R_{2}, R_{3}, and R_{5}, and Z_{4} comprises capacitor C_{4}, then the input impedance, Z_{IN}, appears as a virtual inductor of value L_{IN}:

Figure 2 shows the GIC circuit in its dc configuration. When you consider the GIC circuit in a purely dc environment, you can envision new applications. For example, you could replace impedances Z_{1} through Z_{5} with pure resistances R_{1} through R_{5}. Instead of an ac input-voltage source, connect a precision temperature- and time-stable dc reference voltage to the input port. A simple circuit analysis using ideal op amps for IC_{1} and IC_{2} shows that the reference input voltage, V_{REF}, appears across resistor R_{5}, and, as the following equation shows, a constant current, I_{O}, flows through R_{5}.

Figure 2. |
Replacing all of a GIC’s impedances with resistorscreates a constant-current source. |

However, op amp C_{2}'s noninverting input diverts a small amount of current from the junction of R_{4} and R_{5}, and I_{O} thus also flows through R_{4}. Selecting large values for R_{1}, R_{2}, and R_{3} helps minimize current drawn from the reference voltage. For example, the circuit can supply 2 to 10 mA to R_{4} and draw only a few tenths of a microampere from the reference source. Using tight-tolerance and low-drift components for V_{REF} and R_{5} ensures the stability of I_{O}. Applications include providing constant-current drive for Wheatstone-bridge and platinum-element sensors (Reference 2). In addition, you can replace R_{4} with a series of resistive sensors as in an Anderson loop (Reference 3).

## References

- Franco, S, Design with Operational Amplifiers and Analog Integrated Circuits, Third Edition, ISBN 0072- 320842, WCB-McGraw-Hill, 2001.
- Ramírez, Diego, S Casans, and C Reig, "Current loop generated from a generalized impedance converter: a new sensor signal conditioning circuit," Review of Scientific Instruments, Volume 76, No. 1, January 2005.
- Anderson, KF, "Looking under the (Wheatstone) bridge," Sensors, June 2001, pg 105.