There are two basic methods of generating FM waves: indirect method and direct method. In indirect method a NBFM wave is generated first and frequency multiplication is next used to increase the frequency deviation to the desired level. In direct method, the carrier frequency is directly varied in accordance with the message signal. To understand the indirect method it is required to know the generation of NBFM waves and the working of frequency multipliers.
A frequency modulated wave is defined as: (from equation 5.9)
The above equation defines a narrow band FM wave. The generation scheme of such a narrow band FM wave is shown in the fig.(5.8). The scaling factor, (2πk1) is taken care of by the product modulator. The part of the FM modulator shown inside the dotted lines represents a narrow-band phase modulator.
The narrow band FM wave, thus generated will have some higher order harmonic distortions. This distortions can be limited to negligible levels by restricting the modulation index to β < 0.5 radians.
Frequency Multiplier:
The frequency multiplier consists of a nonlinear device followed by a band-pass filter. The nonlinear device used is a memory less device. If the input to the nonlinear device is an FM wave with frequency, fc and deviation, ∆f1 then its output v(t) will consist of dc component and ‘n’ frequency modulated waves with carrier frequencies, fc, 2fc, 3fc, …… nfc and frequency deviations a ∆f1, 2∆f1 , 3∆f1 , ........ n∆f1 respectively.
The band pass filter is designed in such a way that it passes the FM wave centered at the frequency, nfc with frequency deviation n∆f1 and to suppress all other FM components. Thus the frequency multiplier can be used to generate a wide band FM wave from a narrow band FM wave.
Generation of WBFM using Indirect Method:
In indirect method a NBFM wave is generated first and frequency multiplication is next used to increase the frequency deviation to the desired level. The narrow band FM wave is generated using a narrow band phase modulator and an oscillator. The narrow band FM wave is then passed through a frequency multiplier to obtain the wide band FM wave, as shown in the fig:(5.9). The crystal controlled oscillator provides good frequency stability. But this scheme does not provide both the desired frequency deviation and carrier frequency at the same time. This problem can be solved by using multiple stages of frequency multiplier and a mixer stage.
Generation of WBFM by Armstrong’s Method:
Armstrong method is an indirect method of FM generation. It is used to generate FM signal having both the desired frequency deviation and the carrier frequency. In this method, two-stage frequency multiplier and an intermediate stage of frequency translator is used, as shown in the fig:(5.10). The first multiplier converts a narrow band FM signal into a wide band signal. The frequency translator, consisting of a mixer and a crystal controlled oscillator shifts the wide band signal to higher or lower frequency band. The second multiplier then increases the frequency deviation and at the same time increases the center frequency also. The main design criteria in this method are the selection of multiplier gains and oscillator frequencies. This is explained in the following steps.
Fig: 5.10 – Generation of WBFM wave by Armstrong methodDesign Steps:
Q: How to choose n1 and n2 for the given specifications?
1. Select the value of β < 0.5 for the narrow band phase modulator. This value limits the harmonic distortion by NBPM to minimum.
2. The requirement is that the frequency deviation produced by the lowest modulation frequencies is raised to required ∆f. So choose the frequency deviation of NBFM, ∆f1 by selecting the minimum value of fm.
3. Frequency Multipliers change the frequency deviation. Hence the total change in the frequency deviation is product of the two deviations:
4. Frequency Translator (mixer & oscillator) will not change the frequency deviation, it only shifts the FM signal to either upwards and downwards in the spectrum. The output of mixer is
5. Choose suitable value for f2 and solve the equations (b) and (c) simultaneously to find the multiplying factors n1and n2.
Example 5.12: Design Armstrong FM generator for the generation of WBFM signal with Df = 75 kHz and fc = 100 MHz, using the narrow band carrier as 100 kHz and second carrier as 9.5 MHz. Find the suitable multiplying factors. Assume the message signal is defined in the range, 100Hz ~ 15KHz.
Solution:
In direct method of FM generation, the instantaneous frequency of the carrier wave is directly varied in accordance with the message signal by means of an voltage controlled oscillator. The frequency determining network in the oscillator is chosen with high quality factor (Q-factor) and the oscillator is controlled by the incremental variation of the reactive components in the tank circuit of the oscillator. A Hartley Oscillator can be used for this purpose.
The portion of the tank circuit in the oscillator is shown in fig:5.11. The capacitive component of the tank circuit consists of a fixed capacitor shunted by a voltage-variable capacitor. The resulting capacitance is represented by C(t) in the figure. The voltage variable capacitor commonly called as varactor or varicap, is one whose capacitance depends on the voltage applied across its electrodes. The varactor diode in the reverse bias condition can be used as a voltage variable capacitor. The larger the voltage applied across the diode, the smaller the transition capacitance of the diode.
The frequency of oscillation of the Hartley oscillator is given by:
Thus the output of the oscillator will be an FM wave. But the direct method of generation has the disadvantage that the carrier frequency will not be stable as it is not generated from a highly stable oscillator.
Generally, in FM transmitter the frequency stability of the modulator is achieved by the use of an auxiliary stabilization circuit as shown in the fig.(5.12).
The output of the FM generator is applied to a mixer together with the output of crystal controlled oscillator and the difference is obtained. The mixer output is applied to a frequency discriminator, which gives an output voltage proportional to the instantaneous frequency of the FM wave applied to its input. The discriminator is filtered by a low pass filter and then amplified to provide a dc voltage. This dc voltage is applied to a voltage controlled oscillator (VCO) to modify the frequency of the oscillator of the FM generator. The deviations in the transmitter carrier frequency from its assigned value will cause a change in the dc voltage in a way such that it restores the carrier frequency to its required value.
Advantages of FM over AM are:
1. Less radiated power.
2. Low distortion due to mproved signal to noise ratio (about 25dB) w.r.t. to man made interference.
3. Smaller geographical interference between neighbouring stations.
4. Well defined service areas for given transmitter power.
Disadvantages of FM:
1. Much more Bandwidth (as much as 20 times as much).
2. More complicated receiver and transmitter.
Some of the applications of the FM modulation are listed below:
I. FM Radio,(88-108 MHz band, 75 kHz, )
II. TV sound broadcast, 25 kHz,
III. 2-way mobile radio, 5 kHz / 2.5 kHz.
Example 5.13: An FM wave is defined below.
S(t) = 12 sin(6x108 π t + 5 sin1250 πt)
Find the carrier and modulating frequencies, the modulating index, and the maximum deviation of the FM wave. Also find the bandwidth of the FM wave. What power will the FM wave dissipate in a 10 ohm resistor?
Solution: From equation 5.12, we have
s(t) = A cos[2pf t + b sin(2pf
Comparing with the given FM wave,
Carrier frequency = 3x108 Hz = 300 MHz
Modulating signal frequency, fm = 625 Hz Modulation Index, β = 5 ;
Maximum frequency deviation, ∆f = β fm = 3125 Hz.
Using Carson’s rule, Bandwidth = 2(3125 + 625) = 7500 Hz
Power dissipated across resistor = P,
