Armstrong's method of FM generation

Armstrong's method is an indirect method of generating wide-band FM: first a narrow-band FM (NBFM) wave is made with a crystal-controlled phase modulator, then frequency multipliers and a mixer raise the deviation and set the carrier frequency.

 m(t)->[Integrator]->[Balanced]--( Σ )-> NBFM
                     [modulator] ^ -
                         ^       | +
          +--[-90 deg]---+       |
 [Crystal osc fc1]---------------+
          (NB phase modulator)

 NBFM ->[ x n1 ]->[ Mixer ]->[ x n2 ]->[PA]-> WBFM
                      ^
                 [Osc fc2]

Steps

1. NBFM generation: the message is integrated and applied to a balanced modulator with a −90° shifted carrier. The output is added to the carrier, giving

$$s_{NB}(t) \approx A_c\cos\omega_{c1}t - \beta A_c\sin\omega_mt\,\sin\omega_{c1}t, \quad \beta < 0.3$$

which is NBFM. A crystal oscillator keeps $f_{c1}$ very stable. 2. Frequency multiplication (×n₁): a non-linear stage multiplies both carrier and deviation: $n_1f_{c1}$, $n_1\Delta f_1$. 3. Mixer: shifts the carrier down to a convenient value ($n_1f_{c1} - f_{c2}$) without changing the deviation. 4. Second multiplier (×n₂): gives the final carrier $f_c = n_2(n_1f_{c1} - f_{c2})$ and deviation $\Delta f = n_1n_2\Delta f_1$ (e.g. 75 kHz).

Merit: excellent carrier stability (crystal oscillator). Demerit: many multiplier stages; noise and distortion may increase.