APPARATUS :
1. TIMS-301 Modelling System
2. C.R.O (20MHz)
3. Spectrum Analyzer
4. Connecting chords & probes.
AM Signal, S(t) = E(1 + m·cos(μt)) · cos(ωt)
Where, E is the amplitude of the AM signal
μ is the frequency of the message signal (in rad/s)
ω is the frequency of the carrier signal (in rad/s)
m is the modulation index (varies from 0 to 1)
= {A(1 + m·cos(μt))} × {B·cos(ωt)}
= {low frequency term a(t)} × {high frequency term c(t)}
The low frequency term can be considered as:
a(t) = DC + m(t)
Using an adder, we try to keep the modulation index or modulation depth exactly 100%.
For example, if we set DC voltage to A volts and the amplitude of the AC part as A·m, then the ratio is 1 at the adder output, indicating 100% amplitude modulation.
Circuit Diagram
PROCEDURE :
1. Generate a message signal from the AUDIO OSCILLATOR module.
The oscillator outputs sinusoidal signals and a TTL level digital signal. Pass this through an adder which adds a DC voltage and gain.
2. Supply a 100 kHz carrier signal from the MASTER SIGNALS module.
3. Connect the scope to observe input and output signals.
4. Use FREQUENCY COUNTER to set AUDIO OSCILLATOR to ~1 kHz.
5. Switch SCOPE SELECTOR to CH1-B to view message signal.
6. Adjust for a(t) = A(1 + m·cos(μt)) with m = 1.
7. Turn g and G on adder fully anti-clockwise.
8. View adder output at CH1-A.
9. Set gain to produce VDC = +1V.
10. Set AC amplitude to 1V.
11. Connect adder output to input X of MULTIPLIER.
12. Prepare carrier: c(t) = B·cos(ωt)
13. Connect 100 kHz carrier to input Y of MULTIPLIER.
14. Connect MULTIPLIER output to CH2-A.
15. Display 100% modulated AM signal.
Percentage modulation = (Vmax − Vmin) / (Vmax + Vmin) × 100
Modulation factor = (Vmax − Vmin) / (Vmax + Vmin)
17. Vary ADDER gain G to adjust m and observe effect on envelope for m > 1.
Spectrum :
Sidebands of AM are located on either side of the carrier, spaced by ±μ rad/s.
Circuit Diagram for AM Envelope Recovery
PROCEDURE
Connect the AM output to an envelope detector as shown in the figure above. Use the TUNEABLE LPF module as the low-pass filter. The full system will resemble the figure below.