DEPARTMENT OF ELECTRICAL ENGINEERING AND TELECOMMUNICATIONS TECHNOLOGIES

Course :

EET 2140 Communications Electronics

Module 14: PLL for FM demodulation and final review Prepared by: Dr. Djafar K. Mynbaev Spring 2008 D. Mynbaev, EET 2140

Module 14, Spring 2008

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Module 14: Phase-locked loop (PLL) as an FM demodulator; review for final examination • Review of FM • FM demodulator with phase-locked loop (PLL) • Review for the final exam • Reminder: – Final exam will be next week! – Last chance to submit a term project is the next week! – You must bring all your works (quizzes and term project) next week! D. Mynbaev, EET 2140

Key words • Frequency modulation (FM) • Parameters of FM signal • Modulation index and spectrum of FM signal • Voltage-control oscillator as FM modulator • Slope detector as FM demodulator • Phase-locked loop (PLL) circuit • PLL as FM demodulator

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Frequency modulation (review) •Circuit layout and simulation of the processes have been done by using Multisim of Electronic Workbench. •Calculations and graphs for spectral analysis have been done with Microsoft Excel.

D. Mynbaev, EET 2140

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XSC1

Main drawback of AM

G T

A

B

C A

V1 AM

A1

5uV 1kHz 100 Hz

B 1 V/V 0 V V2 WHITE_NOISE

Schematic for simulation of AM transmission with noise.

Generated AM signal.

You will recall that an AM signal carries information by its amplitude. Noise distorts the amplitude of any signal. Thus, the amplitude of a received AM signal will be distorted and wrong information will received. This drawback is caused by the very nature of AM signal and cannot be eliminated by any technological advances. The ultimate solution to this problem is switching to frequency-modulated (FM) transmission.

D. Mynbaev, EET 2140

Transmitted AM signal plus noise.

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XSC1

Main advantage of FM G T

A

B

V1 FM

C

5uV 1kHz 100 Hz

A1

A B 1 V/V 0 V V2 WHITE_NOISE

Schematic for simulation of FM transmission with noise. Transmitted FM signal plus noise.

You will recall that an FM signal carries information by its frequency. Noise distorts the amplitude of any signal, but it doesn’t prevent an FM signal from delivering correct information.As the right top figure shows, we can recover the correct frequency information in spite of heavily present noise. This figure clearly illustrates the main advantage of FM transmission.

Of course, if a signal is buried in noise, as the bottom figure shows, recovering the correct information would be a difficult task. (Please recall yourself about signalto-noise ratio.) D. Mynbaev, EET 2140

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FM signal and its parameters

Information (modulating) signal vM(t) = AM cos (2 fMt)

Frequency of FM signal, fFM(t) = fC + k vM(t) = fC + kFM AM cos (2 fMt), follows the fluctuations in an information signal. Show the maximum, the minimum and instantaneous values of the frequency of the FM signal.

T

D. Mynbaev, EET 2140

Module 14, Spring 2008

Tmi

Tmax

n

6

Magnitude (V)

15 10 5

Modulation index β = 3

0 -5 1

-10 -15 Time (ms)

Magnitude (V)

15 10 5

Modulation index β = 6

0 -5 1 -10 -15 Time (ms)

Sinusoidal FM signals with various modulation indexes. D. Mynbaev, EET 2140

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1.2 of an FM signal Frequency spectrum and bandwidth

AC

1

The frequency spectrum of an FM signal with various modulation indexes. Observe: 1. The higher the modulation index, the greater the number of frequencies the FM signal contains. 2. We have placed the amplitude of value 1 as a reference point in the three bottom figures; this ―yardstick‖ allows us to show the relative value of other amplitudes. In reality, we use as a reference the amplitude of an un-modulated carrier signal, AC, which corresponds to the amplitude shown here at β = 0. (Remember that by definition: mf ≡ β.) D. Mynbaev, EET 2140

0.8 0.6

β =0

0.4 0.2 0

fC

1 1.2

fC

1 0.8

β =1

0.6 0.4 0.2 0 1

fC - fM

1.2

fC + fM

1 0.8 0.6

β =3

0.4 0.2 0 1

f C - 2f M

1.2

f C + 2f M

1 0.8 0.6

β =6

0.4 0.2

0

Module 14, Spring 2008 1

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BW FM

Frequency spectrum and bandwidth of an FM signal The bandwidth of a sinusoidal FM signal can be calculated as BWFM = 2nfM, where n is the highest order of a side frequency and fM is of course the modulating frequency. From the figure at the previous slide, you can see that for β = 1, we have four side frequencies on each side; that is, n = 4. Hence, in this case, BWFM = 2 x 4 fM = 8fM. In fact, the highest- and the lowest-order side frequencies are equal to fn = fC + n fM and fn = fC - n fM, respectively. Bandwidth, by definition, is the range of frequencies a given signal occupies. Therefore, to compute the bandwidth, we need to subtract the lowest frequency from the highest. In our case, we obtain: BWFM = fC + n fM – (fC - n fM) = 2nfM. Note that, in contrast to amplitude modulation, the bandwidth of an FM signal depends on the modulation index and, therefore, relies on the modulating signal. However, it is the peak frequency deviation, Δf, that determines the FM bandwidth.

Higher-order side frequencies usually have very small amplitudes. Thus, in reality, we overestimate the bandwidth we need for practical use. If we neglect those frequencies whose amplitudes are not more than 5% of the amplitude of an unmodulated carrier signal, we can use approximate formula: BWFM ≈ 2(β + 1)fM or BWFM ≈ 2(β + 1) fM = 2(Δf + fM) = 2(kFM AM + fM) This formula is called Carson’s rule. D. Mynbaev, EET 2140

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Frequency spectrum and bandwidth of an FM signal

XSC1

Waveform of an FM signal G A

T

B

XSA1 V1 FM

1V 100k Hz 10k Hz

R1

1kOhm IN

T

FM Ge n

Schematic for simulation of an FM signal [3]. mf ≡ β = 5. Since β = Δf/fM , then Δf = β fM = 5 x 10 kHz = 50 kHz. The spectrum of this FM signal contains 9 side frequencies; thus, n = 9 and BWFM = 2nfM = 18 x 10 kHz = 180 kHz. The use of approximate formula yields BWFM ≈ 2(β + 1)fM = 12 x 10 kHz = 120 kHz. D. Mynbaev, EET 2140

Module 14, Spring 2008

Spectrum of an FM signal (Span 200 kHz, center frequency 100 kHz.)

10

FM modulators

Voltage-controlled oscillator (VCO)

kFM (Hz/V) vFM(t)

vM(t)

How to obtain an FM signal? Use a voltage-controlled oscillator (VCO), which is a device that generates a sinusoidal signal and allows for changing the frequency of this signal by an external voltage. Here, VCO generates a carrier signal. Information (modulating) signal controls the variations in frequency of the carrier signal. The result is a frequencymodulated (FM) signal. This is an example of a direct FM modulator. D. Mynbaev, EET 2140

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Direct FM modulator G A

Variable control input 1kOhm R1

VCO 4

B

T

8 V CC

RST 7 6 2

Mod signal

1V 10k Hz

20k Ohm R2

3 THR TRI

5

5V V cc

CON GND LM555CN

2.8V

Output

OUT

DIS

10k Ohm RL

1

320pF C

VCO (a 555 integrated circuit timer) generates square-wave (pulse) output, which is used as an FM carrier [3]. Here carrier frequency varies according to variations in modulating signal (red sinusoid), which is applied to the control input of a VCO. D. Mynbaev, EET 2140

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FM demodulators

FM demodulator

vFM(t)

vM(t)

An FM demodulator has to recover the original (information) signal from incoming FM signal.

D. Mynbaev, EET 2140

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FM demodulator I (A)

I(A) = IM cos (2 fMt)

Imax (A)

Imin (A) (fFM)min= fC - Δf

ƒC

(fFM)max= fC + Δf

ƒ (Hz)

fFM(t) = fC + kFM AM cos (2 fMt) We can use a resonant circuit to convert frequency variations into amplitude variations. Here, the frequency swing from (fFM)max= fC + Δf to (fFM)min= fC - Δf results in current variations from Imax to Imin. Since this principle of operation is based on using the slope of a resonant curve, the appropriate circuit is called slope detector. D. Mynbaev, EET 2140

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Frequency discriminator v (V) K (Hz/V)

f(t)

f (Hz)

V(t)

The resonance circuit is an example of a frequency discriminator, the circuit is used to convert frequency variations into voltage (current) changes. The above symbol shows the concept and designation of a frequency discriminator with voltage-to-frequency conversion coefficient K (Hz/V)[1]. Clearly, the slope of the linear segment of this graph is given by (1/K) (V/Hz). D. Mynbaev, EET 2140

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FM demodulator – slope detector Resonant circuit converts frequency variations into amplitude variations.

G A

T

B

2kOhm R1

FM

1m H L1

5V 100k Hz 2kHz

1nF C1

G A

B

T

1 2kOhm R1

FM

5V 100k Hz 2k Hz

2 D

1m H L1

D. Mynbaev, EET 2140

1nF C1

20k Ohm R

Recall AM demodulation: Diode rectifies the signal. Module 14, Spring 2008

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FM demodulator – slope detector G A

T

B

1 2kOhm R1

FM

5V 100k Hz 2k Hz

2 2nF Cc

D

1m H L1

1nF C1

20k Ohm R

4nF C

200k Ohm RL

Low-pass R-C filter ―cleans‖ the signal and capacitor Cc blocks the dc component [3].

D. Mynbaev, EET 2140

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PLL FM demodulator • Circuit layout and simulation of the processes have been done by using Multisim of Electronic Workbench.

D. Mynbaev, EET 2140

Module 14, Spring 2008

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Phase-lock loop (PLL) circuit and its use as a FM demodulator: PLL is one of the most widely used electronic component. Of course, it is implemented as an integrated-circuit (IC). We will concentrate on the use of PLL for FM demodulation, which one of the main applications of PLL.

Phase detector (PD) KPD (V/rad)

Error voltage VPD

Low-pass filter (LPF) KLPF (V/V)

Output voltage Vout

VCO initial signal: v’VCO = AVCO cos(2πf + ΘVCO) Input signal: vin = Ain cos(2π f + Θin) VCO output signal vVCO

Voltage-controlled oscillator (VCO) KVCO (rad/(s-V))

Feedback voltage Vout

Principle of PLL operation: PLL is a classical example of a closed-loop (negative-feedback) system. Phased detector compares input and VCO signals and, if there is a difference between them, produces error signal. This error voltage after being ―cleaned‖ by a low-pass filter serves as an output signal of the system. At the same time, this error (output) voltage is presented to voltage-controlled oscillator, which makes the VCO generates such a signal that will reduce the difference between vin and vVCO to zero. Let’s consider two cases: Case 1 when input and VCO signals have the same frequencies but different phases and Case 2 when input and VCO signals have different frequencies. D. Mynbaev, EET 2140 Module 14, Spring 2008 19

Detailed look at the PD operation Case 1: Input and VCO signals have the same frequencies. Phase detector, PD, compares two signals—input and VCO—at every instant. If they are the same, the phase detector produces no error voltage. If they have the same frequencies, but different phase shifts, PD detects a constant difference between them at every moment and generates constant error voltage.

VPD = KPD (Θin – ΘVCO) = constant

D. Mynbaev, EET 2140

Case 2: Input and VCO signals have different frequencies. Phase detector, again, compares two signals at every instant. In this case, since they have different frequencies, PD detects variable difference between them. This difference is the error voltage, VPD, and this voltage varies the same way as the difference between two frequencies changes.

VPD = KPD (fin – fVCO) = variable

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Phase-lock loop (PLL) circuit Two samefrequency signals with different phases as seen by PD

Output PD voltage, VPD (V)

Phase detector (PD) KPD (V/rad)

Voltage VPD = KPD (Θin – ΘVCO)

Low-pass filter KLPF (V/V)

Output voltage Vout = KPD KLPF x (Θin – ΘVCO)

VCO initial signal: vVCO = AVCO cos(2πf + ΘVCO) Input signal: vin = Ain cos(2π f + Θin) VCO output signal vVCO = KVCO AVCO cos(2πf + 0)

Voltage-controlled oscillator (VCO) KVCO (rad/(s-V))

Vout = KPD KLPF x (Θin – ΘVCO)

Principle of PLL operation: Case 1 – Input and VCO signals’ frequencies, f, are the same. VCO is set to generate a sinusoidal signal with frequency f and phase ΘVCO. A phase detector (PD) compares the phases of an input Θin and the VCO ΘVCO signals and produces an error voltage VPD proportional to their difference. After filtering, this error voltage (in this case – dc, as shown in the previous slide in detail) is applied to the VCO, which forces the VCO generates such a signal that reduces the phase difference to zero; that is, Θin – ΘVCO 0. Output voltage is a filtered error voltage. D. Mynbaev, EET 2140

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Output PD voltage, VPD (V)

Phase-lock loop (PLL) circuit

Two signals with different frequencies as seen by PD

Phase detector (PD) KPD (V/rad)

Voltage vPD = KPD (fin – fVCO)

Low-pass filter KLPF (V/V)

Output voltage vout = KPD KLPF x (fin – fVCO)

VCO initial signal: v’VCO = AVCO cos(2πfVCO) Input signal: vin = Ain cos(2π fin)

VCO output signal vVCO = KVCO AVCO cos(2π fint)

Voltage-controlled oscillator (VCO) KVCO (rad/(s-V))

Vout = KPD KLPF x (fin – fVCO)

Case 2 – Input and VCO signals have different frequencies. VCO is set to generate a sinusoidal signal with frequency fVCO. A phase detector (PD) compares the frequencies of an input signal, fin, and the VCO signal, fVCO,and produces an error voltage VPD proportional to their difference. This error voltage after filtering is applied to the VCO, which adjust the VCO signal’s to make fin – fVCO = 0. Since the difference fin – fVCO keeps changing, voltage vout changes accordingly. (Remember, frequency is a derivative of phase, f = dΘ/dt; hence, phase is an integral of frequency. VCO does this integration. D. Mynbaev, EET 2140

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Concept of PLL FM demodulator: How to use this property of PLL to demodulate FM signal? Let’s

FM modulator

recall that for producing an FM signal we have used VCO! The VCO has generated a carrier signal, whereas input—information (modulating) signal—has controlled the variations in frequency of the carrier signal. The result has been a frequency-modulated (FM) signal.

Voltage-controlled oscillator (VCO) kFM (Hz/V) vM(t)

vFM(t)

FM demodulator

An FM demodulator has to recover the original (information) signal from incoming FM signal.

FM demodulator

vFM(t)

vM(t)

If we could reproduce at the demodulator side the voltage that has controlled the VCO in FM modulator, we would obtain the information (modulating) signal. But this is exactly what PLL is doing! D. Mynbaev, EET 2140

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FM input signal: vFM = AC cos(2π fC + kFM AM cos (2 fMt). fFM(t) = fC + kFM AM cos (2 fMt).

Phase detector (PD) KPD (V/rad)

VCO output signal: vVCO = KVCO A cos(2π fFM) = AVCO cos (2π fC + kFM x AM cos (2 fMt).

Output PD voltage, VPD (V)

Concept of PLL FM demodulator

Voltage VPD ~ KPD (fFM – fVCO)

Low-pass filter KLPF (V/V)

Output voltage vout = KPD KLPF vM, where vM is information (modulating signal: vM = AM cos (2 fMt).

VCO initial signal: vVCO = AVCO cos(2πfVCO) Voltage-controlled oscillator (VCO) KVCO (rad/(s-V))

Vout = KPD KLPF vM

A phase detector (PD) compares the frequency of an input FM signal with the frequency generated by a VCO and produces a voltage VPD proportional to their difference. After filtering, this voltage becomes proportional to an information (modulating) signal and this is the detected information signal. This voltage also forces the VCO to track an input FM frequency, thus keeping the process running. D. Mynbaev, EET 2140

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PLL FM demodulator - MultiSim simulation G

FM Input

A

In1

Out

B

In

Recovered Mod Signal Input FM (below) and recovered information (top)signals.

Out

In2 LPF Phas e_De t

100kohm R 300pF C

Fout

FM 10V 100kHz 5kHz

T

V in

V CO

Phase-locked loop (PLL) FM demodulator [3]: Observe that PLL needs some acquisition interval to adjust VCO’s signal to an input FM signal, as the right bottom figure shows. After this stage, the PLL produces the replica of an information signal, the ―copy‖ of a signal that has driven a transmitter’s VCO when FM signal has been produced for transmission. D. Mynbaev, EET 2140

PLL acquisition (capture) stage as reflected at recovered information (top)signals.

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Assignments: 1.

Reading: a.

Textbook: Pages 271-278.

b. Paul Young, Electronic Communication Techniques, 5th Edition, Prentice Hall, 2004: Sections ―Frequency and Phase Modulation: PLL Demodulator‖ and ―Phase-Locked Loops.‖

2.

Homework problems: Chapter 5: ## 23-26.

3.

Carefully review the examples given in this lecture.

4.

Compare the signals recovered by a PLL demodulator and a slope detector and explain the advantage of a PLL demodulator.

References to Module 12: 1.

Jeffrey S. Beasley and Garry M. Miller, Modern Electronic Communication, 9th ed., Prentice Hall, 2007.

2.

Paul H. Young, Electronic Communication Techniques, 5th ed., Prentice Hall, 2004.

3.

Richard H. Berube, Learning Electronics Communications Through Experimentation Using Electronics Workbench Multisim, Prentice Hall, 2002. D. Mynbaev, EET 2140

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Review for the final examination: • • • • • • •

Communications system Filters Crystal oscillators Spectral analysis Amplitude modulation (AM) Noise Frequency modulation (FM)

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Topic: Communications system and frequency response of R, L and C components You must be able to: • Sketch the block diagram of a communications systems and explain the function of each unit; • Explain where the communications electronics reside and what is its function; • Compute the values of XL and XC and sketch their graphs versus frequency; • Show the relationship between VL and VC in phasor and in waveform formats; • Sketch an equivalent circuits for R, L and C components for low-frequency (ƒ 0) and high-frequency (ƒ ∞) input signals. •Explain how R-C circuit can serve as a low-pass filter. •Explain how R-L circuit can serve as a low-pass filter.

D. Mynbaev, EET 2140

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Topic: Passive and active filters

You must be able to: •

For a low-pass R-C filter

•

Explain the principle of operation; •

Compute a critical frequency;

•

Compute Av = Vout / Vin and Θ in general case and at a critical frequency;

•

Determine how the main filter characteristics—Av = Vout / Vin and Θ—will change with changing the values of a filter components R and C.

•

For a high-pass R-C filter compute Av = Vout / Vin and Θ in general case and at a critical frequency;

•

Explain the principle of operation and qualitatively sketch the main characteristics of a band-pass and band-stop filters; Define high-pass, band-pass and band-stop filters; Sketch R-C circuits for high-pass and band-pass filters. Explain the need for active filters. Active filters: Explain the principle of operation, sketch Av = Vout / Vin graph and explain the need and the main advantage of active over the passive filters. Calculate power in dBm; Calculate gain and loss in dB.

• • • • • •

D. Mynbaev, EET 2140

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Topic: Crystal oscillators You must be able to: •

Explain why do we need oscillators in communications system

•

Explain the principle of operation of a crystal oscillator

•

Sketch an equivalent circuit of a crystal oscillator and explain its operation

•

Discuss the quality factor of a crystal oscillator

•

Discuss the main parameters of crystal oscillators

•

Discuss advantages of crystal oscillators as compared to electronic oscillators.

D. Mynbaev, EET 2140

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Topics: Spectral analysis

You must be able to: • • • • • • • •

• • • • • • •

Explain the concept of time domain and frequency domain and Identify signals in these domains; Distinguish between waveform and spectrum of a given periodic signal; Explain the concept of spectral analysis and synthesis; Understand and use for computations the formula for period and frequency of a harmonic signal; Formulate the Fourier theorem; Use the Fourier formula for calculations of coefficients of the Fourier series; Work with Table 1-4 [1] and compute the values of amplitudes of members of the Fourier series of any given signal; Sketch the components of Fourier series given in Table 1-4 [1] in time and frequency domains; Show the spectrum of a signal based on its Fourier series – spectrum analysis; Show the waveform of a signal based on its spectrum – spectral synthesis; Explain the effect of filtering on signals in both time and frequency domains; Compute the amplitudes of output spectral components of a signal presented to a given filter; Sketch the waveforms of given harmonics before and after filtering; Explain harmonic distortion. Compute total harmonic distortion. D. Mynbaev, EET 2140

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Topic: Amplitude modulation. You must be able to: • Identify modulating, carrier and modulated signals and their parameters (amplitudes and periods) in time domain (from waveforms); •Identify the envelopes of a modulated signal; •Compute a modulation index by two methods in absolute number and in percents; •Compute the amplitudes and the frequencies of upper and lower sidebands and the carrier; •Compute the bandwidth of an AM signal; •Compute the power of a carrier and upper and lower sidebands and the total power of an AM signal; •Explain transmission of an AM signal; •Explain how to generate an AM signal; •Discuss the block diagrams of AM transmitter and its operations; •Discuss the problem of AM demodulation; •Sketch the circuit of an AM detector and explain its operation; •Discuss the block diagram of AM superheterodyne receiver and its operation; •Discuss the AM demodulation in frequency-domain presentation. D. Mynbaev, EET 2140

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Topic: Noise You must be able to: •

Define noise and explain how it affects a transmitted signal;

•

Distinguish between external and internal noise and list the sources of the both types of noise;

•

Classify all types of noise you know;

•

List all the the measures to eliminate noise or reduce its harmful effect;

•

Explain what is an external noise and how we can reduce its effect.

•

Explain what is an internal noise and how we can reduce its effect.

•

Explain the specific types (thermal, shot and flicker) of internal noise.

•

Explain the random nature of noise (e.g., can we predict the exact instantaneous value of noise power?)

•

Compute the average noise power, rms noise voltage and power spectral density of thermal, shot and flicker noise;

• •

Define spectral density and explain how noise spectral density relates to noise power; Qualitatively sketch the graph of the power spectral density of flicker, thermal and shot noise;

•

Qualitatively sketch the general graph of noise spectral density of semiconductor devices versus frequency, distinguish among main segments of this graph and name them and explain whether this graph relates to external or internal noise;

• •

Explain the concept and compute signal-to-noise ratio; Explain how signal-to-noise ratio affects the transmission capacity of a communications system and compute this capacity (Shannon’s formula);

•

Explain the concept and compute noise figure and noise ratio. D. Mynbaev, EET 2140

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Topic: Frequency modulation (FM).

You must be able to: •Describe the concept of frequency modulation (FM);

•Describe parameters of an FM signal and calculate average power of an FM signal; •Present the general formula of an FM signal and show the formula for instantaneous value of its frequency; •Calculate peak frequency variations and maximum, minimum and instantaneous frequency values and show these values at the waveform of an FM signal; •Calculate modulation index and show how FM signal waveforms change with changing the value of modulation index, mf (β);

•Describe the spectrum and bandwidth of an FM signal and compute the bandwidth; •Explain the principle of operation of a direct FM modulator; •Explain the principle of operation of an FM demodulator (slope detector); •Explain the principle of operation of a PLL FM demodulator.

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References to all modules: 1.

Jeffrey S. Beasley and Garry M. Miller, Modern Electronic Communication, 9 th ed., Upper Saddle River, N.J.: Prentice Hall, 2008.

2.

Paul H. Young, Electronic Communication Techniques, 5th ed., Upper Saddle River, N.J.: Prentice Hall, 2004.

3.

Robert L. Boylestad, Introductory Circuit Analysis, 11th ed., Upper Saddle River, N.J.: Prentice Hall, 2009.

4.

Thomas L. Floyd, Electronic Devices, 7th ed., Upper Saddle River, N.J.: Prentice Hall, 2007.

5.

Richard H. Berube, Learning Electronics Communications Through Experimentation Using Electronics Workbench Multisim, Upper Saddle River, N.J.: Prentice Hall, 2002.

6.

Djafar K. Mynbaev and Lowell L. Scheiner, Fiber-Optic Communications Technology, Upper Saddle River, N.J.: Prentice Hall, 2001.

7.

Dennis Rody and John Coolen, Electronic Communication, 4th ed., Englewood Cliffs, N.J.: Prentice Hall, 1995.

8.

Liu et al, Analog VLSI: Circuits and Principles, Boston: The MIT Press, 2002.

9.

Joshua Israelohn, ―Noise 101,‖ EDN, January 8, 2004, pp. 41-47 and ―Noise 102,‖ EDN, March 18, 2004, pp. 47-54.

10.

Paul Horowitz and Winfield Hill, The Art of Electronics, 2nd ed., Cambridge University Press, 1995.

11.

Allan R. Hambley, Electronics, 2nd ed., Upper Saddle River, N.J.: Prentice Hall, 2000. D. Mynbaev, EET 2140

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