Eeng 360 1

Chapter 4

Bandpass Circuits

Limiters

Mixers, Upconverters and Downconverters

Detectors, Envelope Detector, Product Detector

Phase Locked Loops (PLL)

Huseyin BilgekulEeng360 Communication Systems I

Department of Electrical and Electronic Engineering Eastern Mediterranean University

Eeng 360 2

Limiters

( ) ( ) cos( ( ))

( ) cos( ( ))

in c

out L c

v t R t t t

v t KV t t

Limiter is a nonlinear circuit with an output saturation characteristic.

It rejects envelope variations but preserves the phase variations.

Eeng 360 3

Mixers Ideal mixer is a mathematical multiplier of two input signals. One of the signals is sinusoidal generated by a local oscillator. Mixing results in frequency translation.

tjinin

cetgtv Re

tetgAtv tjin

c001 cosRe tjtjtj

intj

incccc eeetgetg

A *0

4

tjin

tjin

tjin

tjin

cccc etgetgetgetgA

0000 **0

4

Input signal:

Output:

SSB mixer

*1 1Re

2 2

Eeng 360 4

Mixers (Choosing LO Freq.)

tjin

tj cc etgA

etgtv 00 Re2

Re 022

tjin

tjin

cc etgA

etgA

tv 00 *001 Re

2Re

2

fGdtetgdtetgtgF intj

intj

inin

**

**

If (fc- f0) = 0 Low Pass Filter gives baseband spectrum

If (fc- f0 )> 0 Bandpass filter Modulation is preserved

Filter Output:

If fc>f0 modulation on the mixer input is preserved

If fc<f0 ‘’ needs to be

positive

Complex envelope is conjugated ~ sidebands are exchanged

-f → Upper & lower sidebands are exchanged * → Phase spectrum is inverted

0 00 01 R

2e Re

2c cj t j t

in in

A Av t g t e g t e

0fff cd 0fff cu Up-conversion Down-conversion

Bandpass Filter Baseband/bandpass Filter (fc-f0)

Eeng 360 5

Mixers (Up Converter and Down Converter)

tgA

tg in20

2

00 fff cd

Complex envelope of an Up Converter:

00 fff cu ; 2

02 tg

Atg in - Amplitude is scaled by A0/2

Complex envelope of a Down Converter:

i.e., f0<fc down conversion with low-side injection

- Amplitude is scaled by A0/2

i.e., f0>fc down conversion with high-side injection00 cd fff

tgA

g in*0

2 2 - Sidebands are reversed

from those on the input- Amplitude is scaled by A0/2

Eeng 360 6

Mixer Realizations Without Multipliers

Multiplication operation needed by mixers can be obtained by using a nonlinear device together with a summer.

Multiplication operation needed by mixers can also be obtained by using an analog switch.

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Frequency MultiplierFrequency Multipliers consists of a nonlinear device together with a tuned circuit. The frequency of the output is n times the frequency of the input.

1

1

( ) ( ) cos( ( ))

( ) ( )

( ) cos ( ( ))

( ) ( ) cos( ( ))

Other Terms

( ) ( ) cos( ( ))

in c

ninn

n nn c

nc

no c

v t R t t t

v t K v t

K R t t t

v t CR t n t n t

v t CR t n t n t

Eeng 360 8

Detector Circuits

Detector Circuits

Transmissionmedium

(Channel)

Carrier circuits

Signal processing

Carrier circuits

Signal processing

Information

minput m~

)(~ tg)(tr)(ts)(tg

Detectors convert input bandpass waveform into an output baseband waveform.

Detector circuits can be designed to produce R(t), Θ(t), x(t) or y(t).

• Envelope Detector

• Product Detector

• Frequency Modulation Detector

Eeng 360 9

Envelope Detector Ideal envelope detector: Waveform at the output is a real envelope R(t) of its input

tttRtv cin cos)( 0tRBandpass input:

tKRtvout K – Proportionality ConstantEnvelope Detector Output:

Diode Envelope Detector Circuit

Eeng 360 10

Envelope Detector The Time Constant RC must be chosen so that the envelope variations can be followed.

In AM, detected DC is used for Automatic Gain Control (AGC)

cfRCB

21

MessageDC)(1)()()( tmKAtgKtKRtv cout

Eeng 360 11

Product Detector Product Detector is a Mixer circuit that down converts input to baseband.

Output of the multiplier:

LPF passes down conversion component:

Where g(t) is the complex envelope of the input and x(t) & y(t) are the quadrature components of the input:

fc- Freq. of the oscillator

θ0- Phase of the oscillator

1 0 0 0 0 0 0

1 1cos cos cos cos 2

2 2c c cv t R t t t A t A R t t A R t t t

0 ( )0 0 0

1 1cos Re ( ) ( ) ( ) ( )

2 2j j t

outv t A R t t A g t e g t R t e x t jy t

Eeng 360 12

Different Detectors Obtained from Product Detector

tRAvout 02

1 0 if t

0if 90 ( ) cos cin cv t A t t

txAtvout 02

1 :0 if 0 Oscillator phase synchronized with the in-phase component

We obtain INPHASE DETECTOR.

900 Re

2

1 tjcout eAAtv tAAtv cout sin

2

10The product detector output is or

If the phase difference is small tAAtv cout 02

1 tt sin

90 if 0 tyAvout 02

1 We obtain QUADRATURE PHASE DETECTOR

We obtain ENVELOPE DETECTOR If the input has no angle modulation and reference phase (θ0) =0

We obtain PHASE DETECTOR If an angle modulated signal is present at the input and reference phase (θ0) =90

The output is proportional to the Phase difference (Sinusoidal phase characteristics)

Eeng 360 13

Frequency Modulation Detector

( ) ( )( )

( ) DC AC (Proportional to ( ))

out L c L c

L c L f

d t d tv t V V

dt dt

V V K m t m t

t

fcin dmKttttAtv )()()](cos[)()(

)](cos[)(1 ttVtv cL )](sin[)(

)(2 ttdt

tdVtv ccL

• The DC output can easily be blocked

A ideal FM Detector is a device that produces an output that is proportional to the instantenous frequency of the input.

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Frequency Detector Using Freq. to Amplitude Conversion

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Phase Locked Loop (PLL) PLL can be used to Track Phase and Frequency of the carrier component of the incoming

signal

Three basic components:

- Phase Detector : Multiplier (phase comparator)

- VCO : Voltage Controlled Oscillator

- Loop filter: LPF

Operation is similar to a feedback system

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PLL, Voltage Controlled Oscillator (VCO)

Voltage Controlled Oscillator (VCO):

Oscillator frequency is controlled by external voltage

Oscillation frequency varies linearly with input voltage

If e0(t) – VCO input voltage, then its output is a sinusoid of frequency

(t)=c+ce0(t)

c - free-running frequency of the VCO.

The multiplier output is further low-pass-filtered & then input to VCO

This voltage changes the frequency of the oscillator & keeps it locked.

Eeng 360 17

Phase Locked Loop (PLL)

Let input signal be : )](sin[ )( ttAtv iciin

Let the VCO output be:

The phase detector output v1(t) is given by :

(t)])(sin[2(t)]-)(sin[2

)](cos[ )](sin[ )( 0001 tttAAK

ttttAAKtv icioim

cicoim

2and(t)-(t)(t)where)((t)][sin)( d2

oimoieed

AAKKtfKtv

The sum frequency term is rejected by LPF so the filter output v2(t) is:

e(t) is called the Phase Error. The Phase Error voltage characteristics is SINUSOIDAL.

A PLL can track the incoming frequency only over a finite range Lock/hold-in range

The frequency range over which the input will cause the loop to lock pull-in/capture range

)]([cos )( ttAtv ocoo t

vo dvKt )()( 2

Eeng 360 18

Various types of Phase Detector characteristics used in PLL’s.

Phase Locked Loop (PLL)

Eeng 360 19

PLL used for coherent detection of AM signals.

• A synchronized carrier signal is generated by the PLL.

• VCO locks with 90 phase difference so a -90 extra phase shift is neededextra phase shift is needed.

• The generated carrier is used with a product detector to recover the envelope

Aplications of PLL

Eeng 360 20

PLL used as a frequency synthesizer.

Frequency dividers use integer values of M and N.

For M=1 frequency synthesizer acts as a frequency multiplier.

Aplications of PLL

x outout x

f f Nf f

M N M