Topic: Communication Systems
Two resistors $R_1$ and $R_2$ (in ohms) at temperatures $T_1$ K and $T_2$ K respectively, are connected in series. Their equivalent noise temperature is
- A. $T_1+T_2$
- B. $R_1$
- C. $(R_1T_1+R_2T_2)/(R_1R_2)$
- D. $(R_1T_1+R_2T_2)/(R_1+R_2)$
Answer: D. $(R_1T_1+R_2T_2)/(R_1+R_2)$
Explanation: Noise spectrum across $R_1=2kT_1R_1$.
Noise spectrum across $R_2=2kT_2R_2$.
Total noise spectrum = $2kT_1R_1+2kT_2R_2$.
Equivalent noise temperature = $\frac{\text{Total noise spectrum}}{2k \times \text{Total resistance}}=\frac{2kR_1T_1+2kR_2T_2}{2k(R_1+R_2)}=\frac{R_1T_1+R_2T_2}{R_1+R_2}$.