Chapter 4 Bandpass Circuits Limiters Mixers, Upconverters and Downconverters
description
Transcript of Chapter 4 Bandpass Circuits Limiters Mixers, Upconverters and Downconverters
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
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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.
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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
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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)
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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
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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
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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
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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
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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
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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
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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)
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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.
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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
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Various types of Phase Detector characteristics used in PLL’s.
Phase Locked Loop (PLL)
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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
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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