Topic: Signals and Systems
What is the R.M.S of following waveform if the average value is zero? (A sawtooth-like waveform with peak positive amplitude 4V, and negative peak A occurring at $t=0$, completing a cycle at $T$)
- A. $\sqrt{\frac{17}{3}}\text{ V}$
- B. $\sqrt{\frac{8}{3}}\text{ V}$
- C. $\sqrt{\frac{5}{3}}\text{ V}$
- D. $\sqrt{\frac{1}{3}}\text{ V}$
Answer: C. $\sqrt{\frac{5}{3}}\text{ V}$
Explanation: For the average value to be zero, the area above the time axis must equal the area below. Based on the geometry provided in the solution, solving for the negative peak gives $A = -1$ V. The signal can be described as $x(t) = \frac{8}{T}t - 1$ for $0 \le t \le T/2$ and $x(t) = -1$ for $T/2 < t < T$. The RMS value is $\sqrt{\frac{1}{T} \int_{0}^{T} x²(t) dt}$, which evaluates to $\sqrt{5/3}$ V.