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Spring 2006: RF CMOS Transceiver Design (TSEK-26)
Tutorial-3: Mixer Design
Problem-3.1(Tutorial)
ωRF and ωLO are fed to the ideal mixer shown in figure below.
Draw the spectrum at IF port if mixer is
a) Unbalanced
b) Single Balanced
c) Double-Balanced
d) There are two possibilities for LO signal either it can be a sine wave or square wave. In
which case the conversion gain will be higher if both have equal peak-peak magnitude.
e) What will be the requirement for post-mixing filter for the cases in part d).
Problem-3.2(Tutorial)
Gilbert mixer and its variants are one of the most popular types of mixers used in today’s designs
due to its good conversion gain, NF, linearity and isolation.
VDD
R1
M3 M4
VLO
VRF
R2
VIF
M1
M5 M6
M2
ISS
a) Drive the expression for the conversion gain of double balanced Gilbert mixer.
b) Drive the expression for IIP3 and estimate IIP3 of the mixer, assuming (Vgs0-Vt) = 0.2V
for the transistors of RF port.
c) How much would be IIP3 improved with 50% increase in (Vgs0-Vt)? What would be the
plenty in form of power consumption for this improvement?
Problem-3.3 (Exercise)
Assume that the switching transistors (square wave LO input) in Gilbert mixer are ideal and do
not generate any noise. The only noise generating transistors are RF port transistors.
a) Drive the expression for NF for Gilbert mixer.(Exercise) (Hint: Lecture Notes )
b) Calculate the input referred noise and NF. Assume that RL = 200Ω, RS = 50Ω, γ=2 and
gmRF=7.5mA/V
Electrical Engineering Department (ISY), Linköping University
rashad@isy.liu.se
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Spring 2006: RF CMOS Transceiver Design (TSEK-26)
Problem-3.4 (Tutorial)
Passive mixers have better IM3 performance but higher conversion loss and hence higher noise
figures compared to active mixers. A double balanced passive mixer is shown with square wave
oscillator VLO(t). Assume that VRF(t)= ARF Cos(ωRFt).
RS/2
+
-
LO
Vout
LO
LO
RS
LO
VRF
RS/2
a) Find the conversion gain of mixer in dB if the switches are ideal.
b) Find the conversion gain of mixer in dB if the switches have on resistance of Rs/2.
c) Derive the expression for the device width if the maximum gain degradation is no more
than 1 dB compared to the gain in part a). Assume that the transistor is working in linear
region.
d) Drive the expression for total power consumed by LO in driving the capacitance of all
transistors working as switch.
e) What happens when the LO duty cycle is not 50%, draw the approximate frequency plot
to motivate your answer. (Exercise)
Problem-3.5 (Home Work)
Design a differential input stage (RF stage) of CMOS Gilbert mixer. The mixer should meet
following specifications IIP3=10dBm, NF= 10dB. Assume Kn = 100uA/V2, RL = 200Ω, RS =
50Ω and γ=2.
Electrical Engineering Department (ISY), Linköping University
rashad@isy.liu.se