The Transistor — Question 7

Question 7

A saturated transistor switch requires a chosen forced current gain

An NPN switch drives a $100\,\Omega$ collector load from 5.00 V, with emitter grounded. At saturation use $V_{CE}=.200\,\mathrm V$ and $V_{BE}=.800\,\mathrm V$. A 3.30 V logic source drives the base through $R_B$. Require forced gain $I_C/I_B=10$.

1. Find load current, required base current, and base resistance.

2. Find collector-emitter dissipation and total terminal power including base-emitter input power.

Question 7 - Solution

A saturated transistor switch requires a chosen forced current gain

(a) Method and calculation

$$\boxed{I_C=(5.00-.200)/100=48.0\,\mathrm{mA},\quad I_B=I_C/10=4.80\,\mathrm{mA}}.$$$$\boxed{R_B=(3.30-.800)/.00480=520.8\,\Omega}.$$

(b) Interpretation and further calculation

$$\boxed{P_{CE}=V_{CE}I_C=.200(.0480)=9.60\,\mathrm{mW}}.$$$$\boxed{P_{\mathrm{device}}=V_{CE}I_C+V_{BE}I_B=9.60+3.84=13.44\,\mathrm{mW}}.$$

Physical check

The forced gain is a switching design condition, not the forward-active beta law. In saturation both transistor junctions are forward biased.