#### What is in this article?:

- Microwave Transistor-Parameter Trade-offs in Circuit Design: Part 3
- Output admittance (yoe) to hFE relationship
- Trade-offs
- Large-signal input impedance measurements
- Thermal effects, resistor stabilization and trade-offs
- Summary

**Output admittance (y**_{oe}) to h_{FE} relationship

_{oe}) to h

_{FE}relationship

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Generally, a high-h_{fe} transistor and one of high-output capacitance have low real-output impedance. Actually, the output resistance at high frequencies in a small-signal analysis (simplified) approaches 1/(w_{t}C_{o}), where C_{o }is nearly C_{ob}. Thus, it is expected that where current crowding and current distribution have little effect, a high-dc-beta device will have the lowest output impedance. This is so in Fig. 3, where the parallel-output resistance is lower at low currents for a high-beta device than for one of low-beta. The difference, nevertheless, is rather small; and at high current levels, variations in distribution of the current and current pinch-off effect will probably mask this tendency as it does for these curves.

*Fig. 3.** Output impedance vs collector current curves show that the higher the dc beta the lower the output impedance, particularly at low values of collector current. The effect is not great, however.*

It is important to note on these curves (which represent small-signal measurements of parallel output resistance) that output resistance decreases significantly as the collector current is increased. This provides a clue that the output resistance will be significantly lower in a large-signal circuit of an rf power amplifier than for the small-signal case or where the transistor drive level is low. Thus, the harder a transistor is driven, the lower the output impedance will become. Measurements of large-signal output impedance should bear this out. Output capacitance is fairly constant with current swing but not with voltage.

Collector breakdown-voltage differences will also affect the output impedance. For a single-type transistor, one with a higher BV_{CBO} than another (and thus a higher resistivity) will have a lower output capacitance and subsequently a somewhat higher output impedance. The trade-off, however, is that the higher the collector-base breakdown voltage (and thus the resistivity of the silicon material) the lower the saturated power-output capability of the transistor. This condition increases the saturation voltage level and reduces efficiency as a transistor multiplier.

**Input impedance (Z _{in}) to h_{FE} relationship**

*Fig. 4.** Input circuit representations. Where the input capacitance is large, as for high-power transistors, the general circuit (a) can be simplified to that at (b).*

The input impedance of a transistor at high frequencies can be represented by the simple circuit in Fig. 4a. Assuming the input capacitance is large, as for a high-power rf transistor, the circuit can be reduced to that of a series inductance and a base resistance shown at b. The input capacitance decreases as the dc beta of the device is increased as shown in Fig. 5. Therefore, the hf input inductance becomes effectively smaller as the dc beta becomes greater. This is because the capacitive reactance will be larger and cancel out more of the package and circuit inductance. This is shown in Fig. 6 where the effective small-signal series inductance decreases as the dc beta increases. The large-signal value will also be different from the small-signal value. The inductance due to the package itself is of fixed value.

*Fig. 5. **Input capacitance vs dc beta. The capacitance decreases with increased beta, which means that the hf input inductance (Fig. 4b) becomes less as dc beta increases.*

*Fig. 6.** Series input inductance vs dc beta (small signal). This phenomenon follows from the effect shown in Fig. 5 for input capacitance vs dc beta.*

A high-dc-beta unit would be expected to have a higher base resistance since the lateral sheet resistance of the base under the emitter would be higher. The effect is fairly pronounced as shown in Fig. 7. The base resistance can increase by as much as 25 percent over the beta range of any transistor type. This is a small-signal base resistance and is lower in a large-signal condition.

*Fig. 7.** Base resistance vs dc beta. The lateral sheet resistance of the base under the emitter increases with dc beta.*