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## Q. 3.12

Objective: Design the size of a power MOSFET to meet the specification of a particular switch application.

The load in the inverter circuit in Figure 3.45 is a coil of an electromagnet that requires a current of 0.5 A when turned on. The effective load resistance varies be tween 8 and 10 Ω depending on temperature and other variables. A 10 V power supply is available. The transistor parameters are $k´_{n} = 80 µA/V^{2}$ and $V_{T N} = 1 V$.

## Verified Solution

One solution is to bias the transistor in the saturation region so that the current is constant, independent of the load resistance.
The minimum $V_{DS}$ value is 5 V. We need $V_{DS} \gt V_{DS}(sat) = V_{GS} − V_{T N}$ . If we bias the transistor at $V_{GS} = 5 V$, then the transistor will always be biased in the saturation region. We can then write
$I_{D} = \frac{k´_{n}}{2} \cdot \frac{W}{L} (V_{GS} − V_{T N})^{2}$
or
$0.5 = \frac{80 × 10^{−6}}{2} \left(\frac{W}{L} \right) \cdot (5 − 1)^{2}$
which yields W/L = 781.
The maximum power dissipation in the transistor occurs when the load resistance is 8 Ω and $V_{DS} = 6 V$. Then
$P(max) = V_{DS}(max) \cdot I_{D} = (6) \cdot (0.5) = 3 W$
Comment: We see that we can switch a relatively large drain current with essentially no input current to the transistor. The size of the transistor required is fairly large, which implies a power transistor is necessary. If a transistor with a slightly different width-to-length ratio is available, the applied $V_{GS}$ can be changed to meet the specification.