The Transistor — Question 10

Question 10

Charging an insulated gate consumes energy even without dc gate current

Model a transistor gate as constant capacitance $C_g=20.0\,\mathrm{pF}$ charged from 0 to $V_{DD}=3.30\,\mathrm V$ through a resistive driver, then discharged to ground. There is no energy recovery or leakage.

1. Derive energy drawn from the supply during charging and energy stored at the final gate voltage.

2. Find total energy dissipated per complete charge-discharge cycle and average dynamic power at $10.0\,\mathrm{MHz}$ complete cycles per second.

Question 10 - Solution

Charging an insulated gate consumes energy even without dc gate current

(a) Method and calculation

$$E_{\mathrm{supply}}=\int V_{DD}I\,dt=V_{DD}Q=\boxed{C_gV_{DD}^2}.$$$$U_g=\int_0^{C_gV_{DD}}(q/C_g)dq=\boxed{\tfrac12C_gV_{DD}^2}.$$

(b) Interpretation and further calculation

$$E_{\mathrm{cycle}}=\tfrac12C_gV_{DD}^2+\tfrac12C_gV_{DD}^2=\boxed{C_gV_{DD}^2=217.8\,\mathrm{pJ}}.$$$$\boxed{P_{\mathrm{dyn}}=fC_gV_{DD}^2=2.178\,\mathrm{mW}}.$$

Physical check

Half the supply energy is dissipated during charging and the stored half during discharge. Zero steady gate current does not mean zero switching power; actual gate capacitance can vary with bias.