# Calculations and Simulations with Pads and Feedback Amplifiers

(R9 is a dummy resistor that keeps SPICE happy — the simulator program does not “like” an open circuited voltage generator.) This circuit for the examination of the amplifier input scattering parameter, S11, which is the input voltage reflection coefficient, was discussed in a short 1993 QEX paper, Reflections on the Reflection Coefficient, and is paper #33 on the EMRFD CD. The degeneration resistance, R7, is set at 6 Ohms for all of the simulations presented.

The AC voltages are set to sweep from 1 to 100 MHz. A result of this analysis is shown below:

This plot shows the input reflection coefficient plotted over the 1 to 100 MHz region. It is in dB form, which is known as the input scattering parameter, S11, in dB form. The negative of this is Return Loss.

The input match, S11, is numerically evaluated by double clicking on the V(S11) from the SPICE program. (Not here — sorry.) The result at 10 MHz is |S11|= -19.9 dB. (Return loss is, hence, 19.9 dB.) The angle shown at 10 MHz is -112 degrees. The dB return loss value is converted to a voltage reflection coefficient of 0.0102 at -112. The reflection coefficient is converted to an impedance with MicroSmith, which yields Z-in at 10 MHz of 49.6 – j 0.939. This corresponds to a 49.6 Ohm resistor paralleled by a 6 pF capacitor.

The analysis also shows a forward gain of S21=21.3 dB. The input match, S11, is a function of the feedback elements (R3 and R7) as well as the coupling coefficient K for the windings in the collector transformer.

### An Amplifier with a Narrow Band Load.

The analysis above uses a 50 Ohm resistor as the load. It is coupled to the amplifier through a 2:1 turns ratio transformer, usually realized in practice with a bifilar winding on a ferrite toroid. (Typical transformer is 12 bifilar turns #28 on a FT-37-43 toroid core.) The input match is reasonable over the whole HF spectrum. We often want to use an amplifier like this in a receiver to drive a narrow band load, such as a filter.

So we ask what happens if a narrow band load is used? This was evaluated by inserting an inductor in series with the load, shown below.

C4 was changed from a 0.1 uF to 126.7 pf, which resonates with L3 at 10 MHz. This results in a drastically different input impedance, shown below, where the sweep range is now reduced to span from 8 to 12 MHz.