Modulation methods used for R.F. telemetry are as follows:

• Amplitude Modulation
• Frequency modulation

Amplitude Modulation: The amplitude of the carrier signal is varied continuously according to the instantaneous value of the modulation signal keeping frequency and phase constant.

Let the carrier signal and modulating signal are given as follows

Carrier Signal: $ e_c=E_c \sinω_ct$

Modulating signal: $e_m=E_m \sinω_mt$

The amplitude of modulated signal is given by

$A=E_c + E_m \sin w_mt\\[2ex] A= E_c + mE_m \sin w_mt \\[2ex]where, E_m = mE_c \\[2ex]A= Ec (1 + m \sin w_mt)$

Hence the instantaneous value of amplitude modulated signal is given by

$e_{AM}= A \sin \omega_ct = Ec\ (1 + m \sin \omega_mt) \sin \omega_ct$

$e_{AM}= E_c \sin \omega_ct + m\ E_c \sin \omega_ct. \sin\ \omega_mt$

$e_{AM}= E_c\ \sin\ \omega_ct + \dfrac{m\ E_c}{2} \cos (\omega_c-\omega_m) t- \dfrac{m\ E_c}{2} \cos (\omega_c-\omega_m) t$

$e_AM=E_c\sin\ 2 \pi\ f_ct + \dfrac{mE_c}{2}\ [\cos\ 2\pi (f_c\ – f_m) t- \cos 2\pi (f_c+f_m)t]$

$Here \ m= modulation \ index (m= E_m/E_c)$

The carrier frequency is also called as center frequency (fc), the two frequencies (fc - fm) and

(fc + fm) are called as lower band frequency and upper band frequency.

Frequency Modulation: The frequency of the carrier signal is varied continuously according to the instantaneous value of the modulation signal keeping amplitude and phase constant.

Let the instantaneous frequency of the modulated wave is given by

$f = f_c (1+KE_m \cos\omega_mt)$

where,Em cosωmt = instantaneous value of modulating signal

         fc= Carrier Frequency

Maximum frequency deviation is achieved when cosine has its maximum value, thus it is given by;f = fc (1+KEc)

Hence maximum deviation is given by;

$δ= KE_cf_c$

The instantaneous value of modulated signal is given by,

$e_{FM}\ =\ A\ \sin\ [\omega_ct\ +\ \dfrac{d}{f_m}\ \sin\ \omega_mt]$

Thus the modulation index is defined as

$m_f\ =\ \dfrac{Maximum\ frequency\ deviation}{Modulating\ frequency}\ =\ \dfrac{ \delta}{f_m}$

Hence the expression for instantaneous modulated signal is given by,

$e_{FM}\ = A\ \sin\ [\omega_ct + m_f \ \sin\ \omega_mt]$