Exercise EE1-03.R3

Prof. Dr. Thorsten Jungmann (last updated 2025-12-09)

Relates to EE1-03 Sources

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Task

A radio transmitter for amateur radio operation has the following ratings:

• Maximum RF output power: $P_{\mathrm{hf},\mathrm{rated}}=100\mathrm{W}$
• Efficiency at maximum power: $\eta =60\%$
• Rated supply voltage: $U_{\mathrm{rated}}=13.8\mathrm{V}$ (vehicle electrical system)

The transmitter is connected directly to a car battery via a cable of length $l=3\mathrm{m}$ with a cross-section of $A=2.5{\mathrm{mm}}^2$ made of copper ($\rho =1.68\cdot 10^{-8}\mathrm{\Omega }\cdot \mathrm{m}$).

Electrically, the transmitter behaves like an ideal resistor (simplified model).

a) What electrical input power $P_{\mathrm{in},\mathrm{rated}}$ does the transmitter require in rated operation?

b) What current $I_{\mathrm{rated}}$ does the transmitter draw in rated operation? Determine the input resistance $R_{\mathrm{TX}}$ of the transmitter.

c) Calculate the resistance $R_{\mathrm{cable}}$ of the connecting cable (outgoing and return conductors).

d) The car battery used has an open-circuit voltage of $U_0=12.6\mathrm{V}$ and an internal resistance of $R_i=15\mathrm{m\Omega }$. Taking all resistances into account, calculate the actual current $I$ and the actual voltage $U_{\mathrm{TX}}$ at the transmitter.

e) What RF output power $P_{\mathrm{hf}}$ can the transmitter still deliver under these conditions?

f) Set up the power balance under these conditions to check whether the power delivered by the source matches the power of the loads.

Solution

a) $P_{\mathrm{in},\mathrm{rated}}\approx 167\mathrm{W}$
b) $I_{\mathrm{rated}}\approx 12.1\mathrm{A}$; $R_{\mathrm{TX}}\approx 1.14\Omega$
c) $R_{\mathrm{cable}}\approx 40\mathrm{m\Omega }$
d) $I\approx 10.5\mathrm{A}$; $U_{\mathrm{TX}}\approx 12.0\mathrm{V}$
e) $P_{\mathrm{hf}}\approx 76\mathrm{W}$
f) $P_{\mathrm{battery}}\approx 133\mathrm{W};P_{{\mathrm{R}}_{\mathrm{i}}}\approx 1.7\mathrm{W};P_{\mathrm{cable}}\approx 4.5\mathrm{W};P_{\mathrm{TX}}\approx 126\mathrm{W}$

Full solution