Download Systematic Design of Space-Time Trellis Codes for Wireless

ECE 4371, Fall, 2016
Introduction to Telecommunication
Engineering/Telecommunication Laboratory
Zhu Han
Department of Electrical and Computer Engineering
Class 5
Sep. 6th, 2016
FM Modulator and Demodulator


Review of FM
FM modulator
– Direct FM
– Indirect FM

FM demodulator
– Direct: use frequency discriminator (frequency-voltage
converter)
– Ratio detector
– Zero crossing detector
– Indirect: using PLL

Superheterodyne receiver
FM broadcasting and Satellite radio
Project 1


Review of last class

PLL and math

Instantaneous frequency

FM and PM
LPF
1 di (t )
fi (t ) 
2 dt
s(t )  Ac cos  2 f ct  2 k f

VCO

m
(

)
d

0

t
s (t )  Ac cos  2 f ct  k p m(t ) 

Modulation index

Narrow band FM characteristics

Carson’s rule
max | ka m(t ) |
,
1
max | k f m(t ) |
FM (frequency):  
fm
AM (envelope):
BT  2f  2 f m  2(  1) f m
FM Direct Modulator

Direct FM
– Carrier frequency is directly varied by the message through
voltage-controlled oscillator (VCO)
– VCO: output frequency changes linearly with input voltage
– A simple VCO: implemented by variable capacitor
– Capacitor Microphone FM generator
FM Direct Modulator cont.

Direct method is simple, low cost, but lack of high stability &
accuracy, low power application, unstable at the carrier frequency
Capacitance changes with
the applied voltage:
C (t )  C0  Cm(t )
LC oscillator frequency:
1
1
fi (t ) 

2 LC 2 LC0  LCm(t )
 C

2
1

m
(
t
)

O
(
t
)


 2C0

f 0 C
 f0 
m(t )
2C0

1
2 LC0
 f 0  f m(t )

Modern VCOs are usually implemented as PLL IC

Why VCO generates FM signal?
Indirect FM

Generate NBFM first, then NBFM is frequency multiplied for
targeted Δf.

Good for the requirement of stable carrier frequency

Commercial-level FM broadcasting equipment all use indirect
FM

A typical indirect FM implementation: Armstrong FM

Block diagram of indirect FM
Indirect FM cont.

First, generate NBFM signal with a very small β1
m(t)  f mt )
v(t )  Ac cos(2 f1t )  1 Ac sin(2 f1t )sin(2
Indirect FM cont.

Then, apply frequency multiplier to magnify β
– Instantaneous frequency is multiplied by n
– So do carrier frequency, Δf, and β
– What about bandwidth?
fi
right
 n fi
left
Analysis of Indirect FM
t

1. Input: v(t )  Ac cos 2 f1t  2 k f  m( )d  ,


0
max | k f m(t ) |
where fi (t )  f1  k f m(t ),  
W
1
2. Nonlinear device outputs frequencies: nf1  nk f m(t )
vo (t )  a1v(t )  a2v 2 (t ) 
 anv n (t ) 
3. Bandpass filter select new carrier f c  nf1
t

s(t )  Ac cos 2 nf1t  2 nk f  m( )d 


0
where new fi (t )  nf1  nk f m(t ),  
max | nk f m(t ) |
W
Armstrong FM Modulator

Invented by E. Armstrong, an indirect FM

A popular implementation of commercial level FM

Parameter: message W=15 kHz, FM s(t): Δf=74.65 kHz.

Can you find the Δf at (a)-(d)?
Solution:
(a) f  14.4 Hz. (b) f  72 14.4  1.036 kHz.
(c) f  1.036 kHz. (d) f  72 1.036  74.65 kHz.
FM Demodulator

Four primary methods
– Differentiator with envelope detector/Slope detector

FM to AM conversion
– Phase-shift discriminator/Ratio detector

Approximates the differentiator
– Zero-crossing detector
– Frequency feedback

Phase lock loops (PLL)
FM Slope Demodulator

Principle: use slope detector (slope circuit) as frequency
discriminator, which implements frequency to voltage
conversion (FVC)
– Slope circuit: output voltage is proportional to the input frequency.
Example: filters, differentiator
freqency in s(t)
10 Hz
20 Hz
voltage in x(t)
j 20
j 40
FM Slope Demodulator cont.

Block diagram of direct method (slope detector = slope circuit +
envelope detector)
t

s(t )  Ac cos 2 f ct  2 k f  m( )d  , where f i (t )  f c  k f m(t )


0
Let the slope circuit be simply differentiator:
t

s1 (t )   Ac  2 f c  2 k f m(t )  sin 2 f ct  2 k f  m( )d 


0
so (t )   Ac  2 f c  2 k f m(t ) 
so(t) linear with m(t)
Slope Detector
Magnitude frequency
response of
transformer BPF.
Bandpass Limiter

A device that imposes hard limiting on a signal and contains a
filter that suppresses the unwanted products (harmonics) of the
limiting process.

Input Signal
t
vi (t )  A(t ) cos (t )  A(t ) cos( wct  k f  m(a)da)



Output of bandpass limiter
Bandpass filter
4
1
1

vo (t )   cos  (t )  cos 3 (t )  cos 5 (t ) 

3
5

eo (t ) 

4

t
cos( wc t  k f  m(a)da)
Remove the amplitude variations

Ratio Detector

Foster-Seeley/phase shift discriminator
– uses a double-tuned transformer to convert the instantaneous frequency
variations of the FM input signal to instantaneous amplitude variations. These
amplitude variations are rectified to provide a DC output voltage which varies
in amplitude and polarity with the input signal frequency.
– Example

Ratio detector
– Modified Foster-Seeley discriminator, not response to AM, but 50%
Zero Crossing Detector
FM Demodulator PLL

Phase-locked loop (PLL)
– A closed-loop feedback control circuit, make a signal in
fixed phase (and frequency) relation to a reference signal


Track frequency (or phase) variation of inputs
Or, change frequency (or phase) according to inputs
– PLL can be used for both FM modulator and demodulator

Just as Balanced Modulator IC can be used for most amplitude
modulations and demodulations
PLL FM

Remember the following relations
– Si=Acos(wct+1(t)), Sv=Avcos(wct+c(t))
– Sp=0.5AAv[sin(2wct+1+c)+sin(1-c)]
– So=0.5AAvsin(1-c)=AAv(1-c)
Superheterodyne Receiver

Radio receiver’s main function
– Demodulation  get message signal
– Carrier frequency tuning  select station
– Filtering  remove noise/interference
– Amplification  combat transmission power loss

Superheterodyne receiver
– Heterodyne: mixing two signals for new frequency
– Superheterodyne receiver: heterodyne RF signals with local tuner,
convert to common IF
– Invented by E. Armstrong in 1918.
Advantage of superheterodyne receiver

A signal block (of circuit) can hardly achieve all: selectivity, signal
quality, and power amplification

Superheterodyne receiver deals them with different blocks

RF blocks: selectivity only

IF blocks: filter for high signal quality, and amplification, use circuits
that work in only a constant IF, not a large band
FM Broadcasting

The frequency of an FM broadcast station is usually an exact
multiple of 100 kHz from 87.5 to 108.5 MHz . In most of the
Americas and Caribbean only odd multiples are used.

fm=15KHz, f=75KHz, =5, B=2(fm+f)=180kHz

Pre-emphasis and de-emphasis
– Random noise has a 'triangular' spectral distribution in an FM
system, with the effect that noise occurs predominantly at the
highest frequencies within the baseband. This can be offset, to a
limited extent, by boosting the high frequencies before transmission
and reducing them by a corresponding amount in the receiver.

Block diagram and spectrum

Relation of stereo transmission and monophonic transmission
FM Stereo Multiplexing
Fc=19KHz.
(a) Multiplexer in
transmitter of FM stereo.
(b) Demultiplexer in
receiver of FM stereo.
Backward compatible
For non-stereo receiver
TV FM broadcasting
 fm=15KHz,
f=25KHz, =5/3, B=2(fm+f)=80kHz

Center fc+4.5MHz

Eye cells structure
XM vs. Sirus
Frequency Allocation
ECE 4371 Fall 2008
Project 1

Project 1
– AM/FM/Real voice
– Due 9/28/16