 fre- given by Equation 18.43, where A Q is the maximum deviation of quency difference f.. If the interfering voltage V cos (w/C + is angular frequency. added to the carrier V C cos wit, the resultant is as in Equation 18.39. (18.43) Vcwc(wi) Thus, the ratio between the output interference and signal voltages is as in Equation 18.44. (18.39) The first term represents amplitude modulation of the carrier and the second term represents a phase displacement, Qj (t), given by Equation 18.40. (18.44) (18.40) For a large modulation index, AS>w_.Thus, as shown in Figure 18.14(b), the output signal to interference ratio is much greater than V.Nx. It is therefore much better than that obtained with AM, the SO Equation 18.41 may be obtained. improvement being proportional to the modulation index A S / "mi If the interference is at the same frequency as the carrier (which (18.41) is the worst situation for AM), Equation 18.44 shows that there is zero interference present at the receiver output. Thus, when two transmissions at the same frequency are received, the output corre- sponds to the stronger. This is known as the capture effect. For FM, the demodulated output voltage is proportional to dqp/dt. Gaussian noise can be considered as consisting of an infinite Thus, the output voltage due to the interference is as in Equation 18.42, for values of f within the pass band of the receiver's output number of interference components, V (q) (where q=0, 11, 22,...), low pass filter, which corresponds to the baseband (Fm) to be spaced at infinitesimal intervals 8 W. Since V w1, the noise handled. If f,>Fm, no interference reaches the output. spectrum at the output of the receiver is parabolic, i.e. the noise power density increases with the square of the frequency. (18.42) The power of each component, V (q), is equal to the noise power in its frequency band, giving Equation 18.45 where n is the input noise power density. Frequency and phase modulation 18/11 Figure 18.14 Effect of interfering signal on FM receiver: (a) phasor diagram