---
title: "Power saving of SSB at 100% and 50% modulation"
subject: "Communication Systems"
chapter: 2
key: "semester_6/communication_systems:ssb-power-saving"
source: https://www.bctengineer.com/q/semester_6/communication_systems/ssb-power-saving
site: BCT Engineering
---

# Power saving of SSB at 100% and 50% modulation

Communication Systems · Chapter 2: Amplitude Modulation

- Asked in: 2068 Bhadra (CS I), 4+4 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/communication_systems/ssb-power-saving
- Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-2

## Question

Determine the percentage power saving of SSB modulated wave for modulation depth equal to: (i) 100%, and (ii) 50%.

## Short answer

For 100% modulation, SSB power saving is 83.33%; for 50% modulation, saving is 94.44%. Saving is computed from P_DSBFC = Pc(1+mu^2/2) and P_SSB = Pc mu^2/4, then (P_DSBFC - P_SSB)/P_DSBFC.

## Answer

Power saving is measured against conventional DSB-FC AM with the same carrier and modulation index.

#### Formulas

With carrier power $P_c = A_c^2/2$ and modulation index $\mu$:

$$
P_{DSB\text{-}FC} = P_c\left(1 + \frac{\mu^2}{2}\right), \qquad P_{SSB} = P_c\frac{\mu^2}{4}
$$

since one sideband has power $\left(\frac{\mu A_c}{2}\right)^2/2 = P_c\mu^2/4$.

$$
\text{Saving} = \frac{P_{DSB\text{-}FC} - P_{SSB}}{P_{DSB\text{-}FC}} = \frac{1 + \frac{\mu^2}{2} - \frac{\mu^2}{4}}{1 + \frac{\mu^2}{2}} = \frac{4 + \mu^2}{4 + 2\mu^2}
$$

#### (i) $\mu = 1$ (100%)

$$
\begin{aligned}
P_{DSB\text{-}FC} &= P_c(1 + 0.5) = 1.5P_c \\
P_{SSB} &= 0.25P_c \\
\text{Saving} &= \frac{1.5 - 0.25}{1.5} = \frac{1.25}{1.5} = 0.8333 = 83.33\%
\end{aligned}
$$

#### (ii) $\mu = 0.5$ (50%)

$$
\begin{aligned}
P_{DSB\text{-}FC} &= P_c(1 + 0.125) = 1.125P_c \\
P_{SSB} &= \frac{0.25}{4}P_c = 0.0625P_c \\
\text{Saving} &= \frac{1.125 - 0.0625}{1.125} = \frac{1.0625}{1.125} = 0.9444 = 94.44\%
\end{aligned}
$$

**Answer:** power saving = **83.33%** at 100% modulation and **94.44%** at 50% modulation.

The saving is larger at low modulation because most of the DSB-FC power is in the carrier, which SSB does not send.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Against which wave is the SSB power saving measured here?
   A. DSB-SC with the same modulation index
   B. DSB-FC with the same carrier and modulation index
   C. An unmodulated carrier
   D. FM with the same bandwidth
   Answer: B. The saving is the power reduction relative to conventional DSB-FC AM. (Key point: Reference for saving)

2. With carrier power Pc, what is the power of an SSB wave (one sideband) for a tone?
   A. Pc μ^2/4
   B. Pc μ^2/2
   C. Pc(1 + μ^2/4)
   D. Pc μ^2
   Answer: A. One sideband has amplitude μAc/2, so its power is (μAc/2)^2/2 = Pc μ^2/4. (Key point: SSB power)

3. What is the percentage power saving at μ = 1?
   A. 66.67%
   B. 94.44%
   C. 75%
   D. 83.33%
   Answer: D. DSB-FC = 1.5Pc, SSB = 0.25Pc, so saving = 1.25/1.5 = 83.33%. (Key point: Result at 100% modulation)

4. Why is the saving larger at 50% modulation (94.44%) than at 100%?
   A. SSB uses more power at low modulation
   B. Most DSB-FC power is in the carrier, which SSB does not send
   C. The bandwidth of SSB shrinks
   D. The sidebands become larger at low μ
   Answer: B. At low μ the carrier dominates DSB-FC power, and SSB does not transmit it, so the saving grows. (Key point: Why saving is larger at low μ)

## Related in Communication Systems

- [Why SSB preferred; AM power at 100% modulation](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Assb-preferred-am-power-1000w) — Communication Systems, chapter 2
- [AM wave diagram, modulation index; why near 100%](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aam-diagram-index-100-percent) — Communication Systems, chapter 2
- [SSB wave for a low pass message signal](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Assb-lowpass-message) — Communication Systems, chapter 2
- [AM transmitter 10 kW/11.8 kW: modulation index and power](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aam-10kw-11-8kw) — Communication Systems, chapter 2
- [Angle modulated signal 12 sin(10⁶t + 5 sin10⁴t)](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aangle-mod-12sin-numerical) — Communication Systems, chapter 3
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