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A carrier sine wave signal and a modulating signal were used to calculate the modulation index and percentage modulation using different values of the modulating sine wave voltage (1Vp, 500mV and 1µV). This was done by computing and comparing the expected values and the values obtained experimentally. The computation helped to us to draw a conclusion and analyze both our results precisely.
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A frequency modulation circuit was used for different modulation indexes (5 and 0) to show the time domain and frequency domain plots as well as verify if the respective plots will yield back the same value
of the modulation index which was used on the signal generator. The values obtained were compared with expected values and a conclusion was drawn with respect to the comparison.
Table of Contents
Abstract..................................................................................................................................................... 2
Introduction....................................................................................................................................................
Theory..................................................................................................................................................... 4
Theory Modulation refers to a process of translating the baseband message signal to bandpass (modulated carrier) signal at frequencies that are very high compared to the baseband frequencies. Frequency modulation is a type of angle modulation and can be defined as maintaining a constant carrier amplitude and varying the carrier frequency with the amplitude of the modulating signal.
Frequency Deviation (δm) is the amount of change in carrier frequency produced by the modulating signal. The frequency deviation can be computed by the equation below,
δm =
where f 2 = fmax
f 1 = f (^) min
(FM modulated signal)
Frequency Modulation index is the ratio of frequency deviation (δ (^) m) to the modulating frequency (f (^) m). One of the issues with the modulation index is that it will vary according to the instantaneous values of deviation and modulating frequency. It can be expressed as follows;
Modulation index(m)=
The bandwidth of a FM signal may be computed using: BW = 2 (β + 1 ) fm =2(fm+^ δm )
Where
β is the modulation index and f (^) m is the maximum modulating frequency used.
Objectives
Materials
Circuit diagram
(frequency modulation)
Procedure The circuit was connected as depicted by the circuit diagram (figure 1) for frequency modulation in the time domain.The function generator was set to a voltage of 5V, offset =0, carrier frequency =1kHz, intelligent frequency = 100Hz, and modulation index= 5. The oscilloscope also set to Time base (scale = 20us/Div, Xpos = 0, Y/T), Ch A (scale =1V/Div, Xpos = 0, DC), Trigger (Pos edge, level=0, Auto). Afterwards I ran the circuit and displayed a frequency modulated carrier on the oscilloscope screen in the time domain, parameters (T 1 and T 2 ) derived from the plot were used to find lowest frequency (f 1 ), highest frequency (f^2 ), frequency deviation^ (δ^ m) and modulation index (m).To display the modulated carrier on the frequency domain a spectrum analyzer was introduced to the circuit and set to a span of 200kHz, center= 100kHz, start=1kHz, end= 101kHz, Range = 0.1 V/Div and a resolution frequency 394,531 Hz. The settings on the function generator were adjusted. Steps 1, 2 and 3 were repeated but this time we changed the modulation index on the function generator to zero only.
Modulation Index set to 0 T 1 =996.622 μs and T 2 =996.622μs (refer to appendix)
f 1 = =1003.389 Hz
f 2 = =1003.389 Hz
Frequency Deviation( δ (^) m )
δm = = 0 Hz
Modulation index(m)
m = = 0
Bandwidth
BW= 2(f m+^ δm )=2(100 + 0)= 200 Hz
Discussion of results
Modulation index deviation = Expected modulation index – obtained modulation index=(5- 4.29)= 0.
Percentage error (%) =
Modulation index deviation =0 and Percentage error (%)= 0%
Expected modulation index
Obtained modulation index
Modulation index deviation
Percentage error(%)
From the circuit which the modulation index was set to 5, when we calculated the modulation index from the curve plot we obtained an m of 4.29 which yielded a percentage error of 14.2% which meant there were very small distortions in the carrier.
For the 0 modulation index both results were equal since there was no modulation giving us a 0% percentage error.
Conclusion
In conclusion the experiment was successful because we managed to show a frequency modulated carrier in the time domain for 0 modulation index and a modulation index of 5 as well as their respective modulating frequencies.
We also gained knowledge on the determination of modulation indexes of a modulated carrier using the time domain display and frequency domain display.
Recommendation
(T 1 displayed by four channel oscilloscope)
(T 2 displayed by oscilloscope)
FREQUENCY DOMAIN OF MODULATED SIGNAL
Modulation index of 0
(T 2 displayed by oscilloscope)
(T 1 displayed by four channel oscilloscope)
