Admittance or Y parameters have been the favorite of many high-frequency analog engineers for many years. Y parameters provide insights into circuit behavior not as apparent as with the more popular S parameters. Although S parameters suit single-stage designs, modeling techniques that are impedance independent--namely Y parameters--suit IC designs best.

Standard Spice models don't accept Y parameters directly, and standard Spice cannot display complex functions such as Y parameters. You must generate special models or subcircuits to accept these Y parameters. Luckily, enhanced versions of Spice can display Y parameters directly.

Figure One

Figure Two

Figs 1 and 2 illustrate methods to extract Y parameters from test-transistor Qtest. Fig 1 pertains to Y₁₁, Y₂₁; Fig 2 covers Y₂₂, Y₁₂. Fig 1a insinuates an image device, Qimage, which is identical to the test device, Qtest.

Qimage is embedded in a closed-loop current-control system comprising the set current-source Iset, current-controlled current-source F1, voltage-controlled current-source G1, and gain-resistor R1. This control system forces the collector current of Qimage to equal Iset. Voltage-controlled current-source G2, which is identical to G1, applies base current to Qtest while maintaining an ac-input open circuit.

Because G1 and G2 are identical and Qtest and Qimage are identical, Qtest's collector current equals Qimage's. Qimage's collector current is, in turn, equal to Iset.

The independent voltage-source Vce supplies collector-to-emitter bias voltage for both transistors while maintaining an ac-output short circuit. Qtest is outside the control system and input ac-current-stimulus Iinput has no effect on bias conditions.

Figs 1b and 1c are plots of Y₁₁ and Y₂₁ vs frequency for Qtest. By definition, Y₁₁ = Iin / Vin and Y₂₁ = Iout / Vin. Therefore, plotting the real and imaginary portions of I(Iinput)/V(Iinput) and I(Vce)/V(Iinput), respectively, (with Voutput shorted to ground by Vce) generates these graphs. (The parametric-analysis feature of pSpice, the enhanced Spice version I used, varied the collector current of Qtest from 1 to 5 mA.)

Extract Y₂₂ and Y₁₂ in a similar manner to that used for Fig 1a. Except in Fig 2a, voltage-controlled voltage-sources E1 and E2 replace voltage-controlled current-sources G1 and G2. And an ac-output voltage-stimulus Vout replaces the ac-input current-stimulus Iinput. E1 maintains an ac short circuit on the input to Qtest, while Vout stimulates Qtest's output. Again, given that Y₂₂ = Iout / Out and Y₁₂ = Iin / Out, plotting the real and imaginary portions of -I(Out) / V(Out) and -I(E1) / V(Out) generates, respectively, the graphs in Figs 2b and c.

You can use an enhanced Spice package's parametric-analysis capability to plot the Y parameters as functions of collector/emitter voltage, temperature, or other parameters. (DI #1563)