--- title: "DSB-FC vs DSB-SC; phase shift method for SSB" subject: "Communication Systems" chapter: 2 key: "semester_6/communication_systems:dsbfc-dsbsc-ssb-phase-shift" source: https://www.bctengineer.com/q/semester_6/communication_systems/dsbfc-dsbsc-ssb-phase-shift site: BCT Engineering --- # DSB-FC vs DSB-SC; phase shift method for SSB Communication Systems · Chapter 2: Amplitude Modulation - Asked in: 2077 Chaitra (CS I), 2+6 marks - Video: [SSB-SC Generation by Phase Shift Method (Basics, Working, Circuit, Block Diagram & Importance)](https://www.youtube.com/watch?v=D6IBERQFP3s) — Engineering Funda - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/communication_systems/dsbfc-dsbsc-ssb-phase-shift - Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-2 ## Question Differentiate DSB-FC and DSB-SC amplitude modulation. Explain phase shift method for the generation of SSB modulated signal with necessary waveform, derivation and diagram. ## Short answer DSB-FC transmits the carrier enabling envelope detection; DSB-SC suppresses the carrier requiring coherent detection. Phase-shift SSB generation uses two balanced modulators: one multiplies message by cosωct, the other multiplies Hilbert-transformed message by sinωct; adding or subtracting cancels one sideband. USB = m(t)cosωct - m̂(t)sinωct, LSB = m(t)cosωct + m̂(t)sinωct. Advantage: no sharp filter; limitation: wideband 90° phase shifter must be accurate. ## Answer #### DSB-FC vs DSB-SC | Point | DSB-FC (conventional AM) | DSB-SC | |---|---|---| | Expression | $A_c[1 + k_am(t)]\cos\omega_ct$ | $A_cm(t)\cos\omega_ct$ | | Carrier | Transmitted | Suppressed | | Power efficiency | Max 33.3% ($\mu=1$) | 100% (all power in sidebands) | | Bandwidth | $2W$ | $2W$ | | Envelope | Follows $m(t)$ if $\mu\le1$ | Does not follow $m(t)$; phase reversals at zero crossings | | Detection | Envelope detector (cheap) | Coherent detector (costly) | | Generation | Square law, switching modulator | Balanced, ring modulator | #### Phase shift method of SSB generation The method uses the Hilbert transform (90° phase shift) to cancel one sideband instead of filtering it. ```text +--->( X )<--- Ac cos wc t | | ^ m(t) -----+ | | Carrier | v | oscillator | (+/-)---> s_SSB(t) | ^ | v | v [-90 deg] | [-90 deg] (HT) | | | | v +--->( X )<--- Ac sin wc t m^(t) ``` Two balanced modulators are used: - Modulator 1: $m(t)$ multiplied by $A_c\cos\omega_ct$. - Modulator 2: $\hat m(t)$ (message shifted by $-90^\circ$) multiplied by $A_c\sin\omega_ct$ (carrier shifted by $-90^\circ$). #### Derivation (single tone) Let $m(t) = A_m\cos\omega_mt$, so $\hat m(t) = A_m\sin\omega_mt$. $$ \begin{aligned} v_1(t) &= A_mA_c\cos\omega_mt\cos\omega_ct = \frac{A_mA_c}{2}[\cos(\omega_c-\omega_m)t + \cos(\omega_c+\omega_m)t] \\ v_2(t) &= A_mA_c\sin\omega_mt\sin\omega_ct = \frac{A_mA_c}{2}[\cos(\omega_c-\omega_m)t - \cos(\omega_c+\omega_m)t] \end{aligned} $$ Subtracting gives USB, adding gives LSB: $$ \begin{aligned} v_1 - v_2 &= A_mA_c\cos(\omega_c+\omega_m)t \quad (\text{USB}) \\ v_1 + v_2 &= A_mA_c\cos(\omega_c-\omega_m)t \quad (\text{LSB}) \end{aligned} $$ In general, $s_{SSB}(t) = A_c[m(t)\cos\omega_ct \mp \hat m(t)\sin\omega_ct]$ (minus: USB, plus: LSB). #### Waveforms / spectra ```text v1 spectrum: LSB USB (both, in phase) v2 spectrum: LSB -USB (USB inverted) v1 - v2: 2*USB -> USB only v1 + v2: 2*LSB -> LSB only ``` **Advantages:** no sharp sideband filter, works for messages with low-frequency content, sideband can be switched easily. **Limitation:** the wideband $90^\circ$ phase shifter must be accurate over the whole message band; any error leaves a residue of the unwanted sideband. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How do DSB-FC and DSB-SC compare in power efficiency? A. DSB-FC is 100% and DSB-SC is 33.3% B. DSB-FC is at most 33.3% (mu = 1); DSB-SC is 100% C. Both are 50% D. Both are 100% Answer: B. The carrier in DSB-FC carries no information and wastes power. (Key point: Efficiency) 2. Which detector suits DSB-FC and which is needed for DSB-SC? A. Coherent for DSB-FC; envelope for DSB-SC B. Envelope for both C. Coherent for both D. Envelope detector for DSB-FC; coherent detector for DSB-SC Answer: D. The DSB-SC envelope does not follow m(t), so coherent detection is required. (Key point: Detection) 3. How does the phase shift method remove one sideband? A. Two balanced modulators with 90° shifted message and carrier are added or subtracted so one sideband cancels B. A very sharp filter blocks one sideband C. The carrier is frequency-doubled D. The message is squared first Answer: A. v1 - v2 gives the USB only and v1 + v2 gives the LSB only. (Key point: Principle of phase shift method) 4. In s = Ac[m cos wc t -/+ m^ sin wc t], which sign gives the USB? A. Plus B. Both signs give USB C. Minus D. Neither; it gives DSB-SC Answer: C. Subtracting gives cos(wc + wm)t, the USB. (Key point: Sign and sideband) ## Related in Communication Systems - [Detection gains of DSB-FC, DSB-SC and SSB](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adetection-gain-dsbfc-dsbsc-ssb) — Communication Systems, chapter 9 - [Compare DSB-AM, DSB-SC, SSB, VSB; SSB by phase discrimination](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Acompare-am-variants-ssb-phase) — Communication Systems, chapter 2 - [Phase shift method of SSB generation: pros and cons](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Assb-phase-shift-pros-cons) — Communication Systems, chapter 2, asked 2× - [Phase shift method of SSB generation](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Assb-phase-shift) — Communication Systems, chapter 2 - [SSB vs AM and DSB-SC; balanced modulator](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Assb-vs-am-balanced-modulator) — Communication Systems, chapter 2 - [DSB-SC vs SSB; synchronous demodulation of DSB-SC](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adsbsc-vs-ssb-synchronous-demod) — Communication Systems, chapter 2