Ring modulator for DSB-SC; characteristics of DSB-SC

A ring modulator is a double-balanced diode modulator in which four diodes form a ring and are switched by the carrier, so the output is the message multiplied by a square wave, which after filtering is DSB-SC.

Circuit

         T1       D1       T2
 m(t) ))|((a-----|>|-----b))|(( --> BPF --> s(t)
        |((  \           /  ))|
        |((   D4       D2   ))|
        |((  /           \  ))|
        )|( d-----|<|----c ))|
          |    D3           |
          +----( c(t) )-----+
         carrier at centre taps

Operation

1. The carrier $c(t)$ is a large square wave (or large sinusoid), $|c(t)| \gg |m(t)|$, so it alone controls the diodes.
2. Positive half cycle of carrier: D1 and D3 are forward biased, D2 and D4 off. The message reaches the output with the same polarity: $v(t) = +m(t)$.
3. Negative half cycle: D2 and D4 conduct, D1 and D3 are off. The paths cross over, so $v(t) = -m(t)$.
4. Hence $v(t) = m(t)\,c(t)$, where $c(t)$ is a ±1 square wave:

$$c(t) = \frac{4}{\pi}\left[\cos\omega_ct - \frac{1}{3}\cos3\omega_ct + \frac{1}{5}\cos5\omega_ct - \dots\right]$$ $$v(t) = \frac{4}{\pi}m(t)\cos\omega_ct - \frac{4}{3\pi}m(t)\cos3\omega_ct + \dots$$

5. Because $c(t)$ has zero mean, there is no carrier term and no baseband term in the output. A band-pass filter at $f_c$ with bandwidth $2W$ gives

$$s(t) = \frac{4}{\pi}m(t)\cos\omega_ct \quad \text{(DSB-SC)}$$

 m(t)   ___
       /   \___
 c(t)  |-| |-| |-|
         |_| |_| |_
 v(t)  m(t) chopped and flipped every half cycle

Basic characteristics of DSB-SC

• Contains only USB and LSB; the carrier is suppressed.
• Bandwidth $= 2W$, same as DSB-FC.
• All transmitted power is in the sidebands: power efficiency 100%. For a tone, power $= P_c\mu^2/2$, a saving of 66.7% vs DSB-FC at $\mu = 1$.
• The envelope is $|m(t)|$; the carrier phase reverses at each zero crossing of $m(t)$.
• Cannot use an envelope detector; needs coherent detection with exact frequency and phase (Costas loop, squaring loop or pilot carrier).
• Used in stereo FM (L−R signal), colour TV chroma, and QAM.