Mixers
EC434
Dr. Amr Bayoumi
EC434 – ASP Fall 2012
(Mixers Lecture)
1
Wireless Transceiver Architecture
LNA
Intermediate
IF Mixer
BPF
Zero IF
Mixer
BPF
VCO
LPF
DEMOD
Baseband
Processing
VCO
PA
BPF
EC434 – ASP Fall 2012
(Mixers Lecture)
LPF
MOD
2
Mixers
• A mixer is mainly a multiplier (usually analog):
A cos(ω 1t) * B cos(ω 2t) = (1/2) AB [cos(ω 1-ω 2)t + cos(ω 1+ω 2)t]
• Down-conversion (Receiver): use (ω 1-ω 2)
• Up-conversion (Transmitter): use (ω 1+ω 2)
• Could be either:
– Intermediate Frequency (IF) : Heterodyne, or
– Direct Conversion (Zero IF): Homodyne
• Needs careful filter design to remove image, out-ofband, and unwanted product terms:
– Both input and output need these filters (Bandpass or Low
pass)
EC434 – ASP Fall 2012
(Mixers Lecture)
3
Building Blocks:
Phase Locked Loop (PLL)
• Local Oscillator (LO) needs to have:
– Same Frequency as incoming signal
– Predetermined phase (0, 90 deg, …) as incoming signal
• Multiplication Equation:
A cos(ω 1t) * B cos(ω 2t) = (1/2) AB [cos(ω 1-ω 2)t + cos(ω 1+ω 2)t]
• Any added phase (ω t + φ ) or frequency drift (ω+∆ )t will alter this
equation
• PLL acts on error with incoming signal to “lock” frequency &
phase
EC434 – ASP Fall 2012
(Mixers Lecture)
4
Building Blocks:
Voltage Controller Oscillators (VCO)
• Local Oscillator (LO) needs to track original signal:
– Same Frequency as incoming signal
– Predetermined phase as incoming signal
EC434 – ASP Fall 2012
(Mixers Lecture)
5
Ideal Case: Multiplier
Multiplier
ω1
ω 1 +ω 2 ,
ω 1 −ω 2
X
ω2
EC434 – ASP Fall 2012
(Mixers Lecture)
6
Practical Case:
Square Law Mixers
Square of sum
ω1, ω2
ω 1 +ω 2 , ω 1 −ω 2
ω1
(V1±V2)
2
2ω 1 , 2ω 2
V1=A cos (ω 1t)
V2= B cos (ω 2 t)
ω2
EC434 – ASP Fall 2012
(Mixers Lecture)
7
Transistor Implementation
Vdd
ZLoad
Vin
Id = K1 (Vgs - Vt)2
= K1 (Vgs2 + Vt2 - 2Vgs Vt )
Vout
RF in
+
Vgs = Vin – VLO = A cos ω 1 t – B cosω 2 t
Vgs2 = Vin2 + VLO2 – 2Vin VLO
Vgs
Vbias
In Saturation:
LC Parallel
Tuning
Circuit
ω1, ω2
VLO
Local Oscillator
Vin2 = (Acosω1t)2
=(A2/2)(1+cos 2ω1t)
ω1±ω2
VLO2 = (Acosω2t)2
EC434 – ASP Fall 2012
(Mixers Lecture)
=(B2/2)(1+cos 2ω2 t)
8
Using Parallel LC as Load (Zload)
(in Previous Circuit)
ZLoad
Inductive
Capacitive
R
Usually there is a parallel R
Which comes from RLoad
and transistor rout
wo
Freq
Gain = -gm ZLoad
Vout = -id ZLoad
Using a parallel LC tank as ZLoad:
ZLoad (ω) = maximum at:
1
ωo =
√ LC
EC434 – ASP Fall 2012
(Mixers Lecture)
Use ω ο = ω 1 ± ω 2
9