Het 314 Communications Principles

HET 314 COMMUNICATIONS PRINCIPLES

LAB 3: ANGLE MODULATION AND DETECTION

LAB REPORT

NAME: HOANG HUNG DINH

STUDENT ID: 6625851

1. AIMS:The purpose of this experiment is to help students understand more about the process of Angle Modulation and also to compare and justify what should we expect between theory and real life about the system. By the end of this experiment, we can see clearly what Angle Modulation is in reality and how to make the system works steps by steps in practice.

2. Theory And Background :Angle Modulation is one type of analog modulation in which the phase angle of the carrier is varied according to the message signal. Two types of Angle Modulation are Phase Modulation (PM) and Frequency Modulation (FM). In this experiment, we only build and analyze Frequency Modulation. Angle Modulation is become really popular because of its advantages.

A Angle Modulation is represented by: y (t) = A co s [ωt+ϕ (t ) ] A Message is used can be represented by: x (t) = Am co s (ωt )

3. Equipment : TIMS Machine, Envelope Detector Box, Multiplier, Adder, 60 kHz LPF and Phase Shifter.

4. Experiment Procedure:In order to generate FM, we divide the experiment into five small sections. We use “Direct method “as mention in the lab manual which is uses a voltage controlled oscillator (VCO) on TIMS unit

1. Frequency Deviation Constant kf :Set up the circuit like a block diagram of connection shown below.

In this part, we have to measure the frequency deviation constant kf for the VCO module on TIMS by measuring the frequency output f0 from varied DC input voltage Vin between +2V and -2V in 0.5 steps and plot that set of data to determine kf and then use kf to calculate the frequency output of a 1.25 V. Take the result and compare with the actual frequency we observe on the screen.

2. Frequency Deviation Δf : In this part, we replace the Voltage input to VCO by the 300 Hz Audio Oscillator module‘s output frequency. Use the Pico Scope to observe the result on the screen. Calculate the peak frequency deviation using formula as follow:

fmin = 1/ Tmax where fmin = minimum frequency and Tmax = maximum period.

fmax = 1/ Tmin where fmax = maximum frequency and Tmin = minimum period.

CS = fmax - fmin where CS = carrier swing.

fmax = maximum frequency

fmin = minimum frequency

Δf = CS/2 where Δf = peak frequency deviation

3. FM Spectrum:Connect the 2 kHz Audio Oscillator module‘s output frequency to the input A of the Buffer Amplifier module and take the output corresponding k1A connect to the input of the VCO. Adjust k1A to observe the spectrum of the VCO. Adjust k1A until the first carrier null and record the result. Compare the actual spectrum to the one in preliminary work.Repeat procedure above for the output frequency of 10 kHz and 300 Hz.

4. FM Detection:Connect the circuit like a block diagram shown below. We got 2sin(4000πt) = 2sin(2000πt)cos(2000πt) + 2sin(2000πt)cos(2000πt) so in order to create the message

Waveform trigger reference

Tc=1/fc

Tmax=1/fmin

Tmin=1/fmax

Message2cos(t)

Multiplier

Carrier2cos(x103t) Phase Shifter

B

g

Audio Oscillator Module

Adder

Output

A

2sin(4000πt) we have to use adder module to add two sin(4000πt) together. In order to make sin (4000πt) we have to use multiplier module to multiply sin(2000πt) and cos(2000πt) and then add two of the product’s result together.

Use a capacitor from the envelope detector box as differentiator.

Record result on the screen

5. Generation Of Narrow-Band Phase Modulation:Connect circuit like block diagram below. Observe result of phase shift 0 to 90 degrees.

5. Results And Discussion:1. Frequency Deviation Constant kf :

At 1.25 V , f0 = 93.8 kHz

Voltage (V) Frequency (kHz)-2 89.7

-1.5 92.5-1 94.9

-0.5 97.80 100.3

0.5 1031 105.7

1.5 108.32 110.9

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.50

20,000

40,000

60,000

80,000

100,000

120,000

f(x) = − 5300 x + 100344.444444444R² = 0.999876075114301

Chart Title

Series2Linear (Series2)

Axis Title

Axis Title

Calculate kf by using formula

We got expression: kf = (100.3-93.8)/-1.25 = 5.2 KHz/v

k f=ΔfΔV

=f c−f 00−V dc

According to the graph we got kf = 5.3 kHz/V

Compare with the actual kf we have error at: 5.3-5.2 = 0.1 KHz/V

2. Frequency Deviation Δf :

Tmax = 9.1 µs ; Tmin = 7.6 µs ; Message Amplitude is 1.984 V

fmin = 1 / (9.1 * 10-6 ) = 109.9 kHz ; fmax = 1 / (7.6 * 10-6 ) = 131.6 kHz

CS = 131.6 – 109.9 = 21.7 kHz so Δf = CS/2 = 21.7 /2 = 10.85 kHz

Using kf and Am measured above we have Δf = kf * Am = 5.3 * 1.984 = 10.52 kHz

Comparing the calculated result with the actual value, we have the different at 0.23 kHz

3. FM Spectrum:

Result for 2 kHz:

Comparing the actual result with the predicted one in preliminary work, we can see they are likely similar. We only got difference between the actual results and the predicted from 0.066 to 0.1, quite small figures.

The spectrum equation is : Ac Jn(β) . if we keep fm constant and changing the amplitude of the modulating Ac therefore spectrum will be changed depend on Ac

Result for 10 kHz:

From the graph we got value of β is 1According to Carson’s rule with β = 1 Bandwidth BT= 2.(1+β)fm = 2 * 2 * 10 = 40 kHz and the result from the graph is exactly the same 120 – 80 = 40 kHz

Result for 300 Hz :

4. FM Detection:

Frequency Domain:

Time Domain:

According to the time domain graph, we can see the message signal in blue has been recovered successfully. Its shape is smoothly recovered and in cosine form. It shifted to the left because of the phase shifter.

5. Generation Of Narrow-Band Phase Modulation:Result for carrier 𝜙 = 0:

Result for carrier 𝜙 = 90:

It’s seemed slightly similar to the DSB-LC modulation and it’s over modulated.

Result for 10 kHz carrier in persist mode:

According to the graph we found the modulation index β is:

β=2π . tT

=2xπx (43.45−41.55)46.45−36.67

=1.22rad

Result for 5 kHz:

We have a bandwidth of 105-95 = 10 kHz

Result for 10 kHz:

We have a bandwidth is 110-90 = 20 kHz

In order to check the bandwidth we can use Carson’s ruleB = 2fm = 2 * 10 = 20 kHz

6. Conclusion:

After went through the whole experiment, we have learned and understood much more about how the Angle Modulation actually builds and processes in real life. We can now justify and compare between what we should expect in theory and what we actually got in practice. Also, from this experiment we knew how to actually build up the demodulation system in order to demodulate the input signal and recover the message signal back.

7. References:Lecture note HET314: Module 8 Angle Modulation.“Electronic communications systems” William Stanley