Ring modulator for DSB-SC

A ring modulator (double-balanced modulator) generates DSB-SC using four diodes connected in a ring, switched ON and OFF by a high-amplitude square-wave carrier. It effectively multiplies the message by a ±1 square wave.

Circuit

            T1        D1        T2
 m(t) o--+ )||( a---->|----b )||( +--o
         | )||( |\       /| )||( |    to
         | )||( | D3   D4 | )||( |    BPF
 o-------+ )||( |   \ /   | )||( +--o
              | |    X    |  |
              | |   / \   |  |
              | c---->|----d  |
              |       D2      |
              +--- c(t) ------+
          (square-wave carrier between
           centre taps of T1 and T2)

(D1 joins a–b and D2 joins c–d: the straight paths. D3 joins a–d and D4 joins b–c: the crossed paths. All four point the same way round the ring.)

Working

• Positive half cycle of carrier: D1 and D2 conduct, D3 and D4 are off. The message passes straight to the output: $v_o = +m(t)$.
• Negative half cycle of carrier: D3 and D4 conduct, D1 and D2 are off. The connections are crossed, so $v_o = -m(t)$.

So the output is $v(t) = m(t)\,c_s(t)$, where $c_s(t)$ is a ±1 square wave of frequency $f_c$.

Derivation

The ±1 square wave (odd harmonics only, zero DC):

$$c_s(t) = \frac{4}{\pi}\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{2n-1}\cos[2\pi f_c(2n-1)t]$$ $$\begin{aligned} v(t) &= m(t)c_s(t) \\ &= \frac{4}{\pi}m(t)\cos\omega_ct - \frac{4}{3\pi}m(t)\cos3\omega_ct + \frac{4}{5\pi}m(t)\cos5\omega_ct - \dots \end{aligned}$$

There is no carrier term and no message term (the square wave has no DC). A band-pass filter centred at $f_c$ with bandwidth $2W$ keeps only

$$s(t) = \frac{4}{\pi}m(t)\cos\omega_ct$$

which is DSB-SC. Condition: $f_c > W$ and in practice $f_c \gg W$ so that the bands at $f_c$, $3f_c$ do not overlap ($3f_c - W > f_c + W$).

Waveforms

 m(t)       ____                ____
           /    \              /
 ---------/------\------------/------> t
                  \____    __/
                       \__/

 c_s(t)    +-+ +-+ +-+ +-+ +-+ +-+
  (+-1)    | | | | | | | | | | | |
          -+ +-+ +-+ +-+ +-+ +-+ +-

 v(t)     m(t) chopped and inverted
          every half carrier cycle

 s(t)     DSB-SC: envelope |m(t)|,
 (BPF)    carrier phase reverses at
          each zero crossing of m(t)

Spectrum

  |V(f)|
     /\        /\         /\
    /  \      /  \       /  \
 --+--+--+---+--+--+-----+--+--+--> f
   (none at 0)  fc       3fc
              (kept)   (removed)

Advantages: carrier and message are both suppressed at the output (double-balanced); good carrier suppression; stable. Requirement: matched diodes and centre-tapped transformers.