ECN 542: Microwave Integrated Circuits

Lecture Module #5: Mixer Design

Karun Rawat
Karun.rawat.in@ieee.org

IIT Roorkee
RF Group, Department of Electronics & Communication Engineering,
Indian Institute of Technology Roorkee, India

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 Important
 These slides have been prepared from several text books and are being
used for class lecture/demonstration only

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 Non-Linear Circuits: Topology
Terminal Nonlinearity Transfer Nonlinearity

 Nonlinear element (R, L, or C) , which  It is non-linear controlled source.

has value function of one independent  The control voltage is somewhere in
variable (V or I) at its terminal. the circuit other than the element’s
 For example, excitation voltage above terminal.
generates non-linear current across the
non-linear element at new frequencies.
 This non-linear current further
generates non-linear voltage across Rs
which corresponds to different
frequency components.
 Rs=0 will restrict this case and voltage
components remain same as
excitation. Courtesy: S. Maas, Non-linear microwave & RF circuits 3/33
 Non-Linear Current:
Power Series Expansion
I  aV  bV 2  cV 3 V  vS  t   V1 cos 1t 
 3 2
i  t   V1  a  cV1  cos 1t 
 4 
V12 V12
b  b cos  21t 
2 2
V13
 c cos  31t   ...
2 4
V1
Pin  if R S  1
2

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Non-linear Components: Resistive Non-
linearity
V12
Pin  if R S  1
2 2
1  3 2 
2
2 3c 
Pout , f  V1  a  cV1    a 1  Pin  Pin
2  4   2a 
  3 c 2 
 GL  1  Pin   Pin
 2 a  
 
2
1 b 2
Pout ,2 f  GL   Pin
2 a Pout ,nf   Pin 
n

2
1 c 3 Pout ,nf (dBm)  nPin  dBm 
Pout ,3 f  GL   Pin
4 a

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 Harmonic Distortion

Pout ,nf
HDnf 
Pout , f
2
1b
HD2 f    Pin
2a
2
1c 2
HD2 f    Pin
4a
Pout ,nf
THD   Sum of all Harmonic Distortions
n2 Pout , f

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 AM/AM and AM/PM Nonlinearity
DPD Charac. DPD Charac.

DPD+PA Charac. DPD+PA Charac.

PA Charac.

PA Charac.

AM/AM: Gain Compression/Expansion AM/PM: Phase Compression/Expansion

 3c 
2
 3 3
G  GL 1  Pin  i1  t    aV1  cV1  cos 1t 
 2a   4 
 For Reactive non-linearity: 1st and 3rd order 3 3
current may not be in phase. I1 1   aV1  cV1 exp  j 
 Even if θ=const., phase (I1) changes with V1 4 7/33
 Linearization &
Quadrature Imperfections

Spectral Mask must be qualified for

transmission.
Predistortion must incorporate I/Q
compensation to work properly. 8/33
 Intermodulation: Two-Tone
I  aV  bV 2  cV 3 VS  vS  t   V1 cos 1t   V2 cos 2t 
ia  t   aV1 cos 1t   aV2 cos 2t 
b 2
ib  t   bv  t   V1  V22  V12 cos  21t   V22 cos  22t 
2
S
2
2V1V cos 1  2  t  cos 1  2  t
c 3
ic  t   bvS  t   V1 cos  31t   V23 cos  31t 
2

4
 3V12V2 cos  21  2  t  cos  21  2  t
 3V1V22 cos 1  22  t  cos 1  22  t
 3 V13  2V1V22  cos 1  t
 3 V23  2V12V2  cos 2  t 9/33
 Intermodulation: Two-Tone
m,n  m1  n2 , m, n  0,  1,  2,...
The k-th term in power series produces new mixing frequency of order k or
below. Not always true if Rs is not zero.
Odd Degree terms produces odd-order mixing product.
Even degree terms generate only even order products.

Courtesy: P. Colantonio et.al., High efficiency RF & Microwave solid state power amplifiers 10/33
 Intermodulation: Two-Tone
m,n  m1  n2 , m, n  0,  1,  2,...
The k-th term in power series produces new mixing frequency of order k or
below. Not always true if Rs is not zero.
Odd Degree terms produces odd-order mixing product.
Even degree terms generate only even order products.

Courtesy: P. Colantonio et.al., High efficiency RF & Microwave solid state power amplifiers 11/33
 Cross Modulation
I  aV  bV 2  cV 3
VS  vS  t   V1 cos 1t   1  m  t  V2 cos 2t 
where, m(t) is a modulating waveform; m t   1
The frequency component at ω1 in third degree term is:

ic  t   cV1V22 1  2m  t   m 2  t  cos 1t  

' 3
2
 A distorted version of modulation of ω2 signal has been transferred to
the ω1 carrier.
 The effect depends strongly upon the magnitude of c and strength of
interfering signal.
 E.g automobile AM radio: passing by radio station modulation comes
on top of other received station. 12/33
 Mixer Fundamentals
 Mixer use a resistive non-linearity to produce an output spectrum
containing the sum and difference frequencies of two input signals.
 Different applications of mixers:

Down converter in Rx

Up converter in Tx

Courtesy: I. Bahl et.al., Microwave Solid state circuit design, Wiley 13/33
 Mixers: Frequency Components (1/2)
 Mixer use a resistive non-linearity to produce an output spectrum
containing the sum and difference frequencies of two input signals.
m,n  mL  nR , m, n  0,  1,  2,...
 The desired mixer output is normally the IF (ωI ), which can be:
I  L  R , lower sideband
I  L  R , upper sideband
 Higher (m, n) products are also called spurious products (or spurs).
 Two possible situations are:
 Case 1: R  L :
IF  L  R , IM  2L  R , Upper _ sideband    L  R
 Case 2: R  L
IF  R  L , IM  2L  R , Upper _ sideband    L  14/33
R
 Mixers: Frequency Components (2/2)
IF  L  R , IM  2L  R , Upper _ sideband    L  R

IF  R  L , IM  2L  R , Upper _ sideband    L  R

Courtesy: I. Bahl et.al., Microwave Solid state circuit design, Wiley 15/33
 Image Enhanced Mixers
 One of the objectives of mixer design is to match desired IF power to
the input of succeeding stage.
 The unwanted frequencies IM ,  should be reflected back
towards the RF input.
 The reflected IM ,  to the diode can undergo another mixing
operation and can add to the IF signal in proper phase to reduce
conversion loss.
 Remixing of image with LO: Image Enhancement
L  IM  L   2L  R   R  L  IF
 Remixing of sum frequency: Sum Enhancement
  2L  R  L  2L  R  L  IF
 The circuit should be arranged such that the various contributions to
the IF signal are all in-phase with IF 16/33
 Mixer Performance Measure (1/6)
1. Conversion Loss:  PRFAvail 
Lmin
C  10 log  Avail 
 PIF 
Theoretical Minimum Value:
4 1 
Vout (t )  VRF sin(RF t )   sin(nLO t ) 
  n 1,3,5..odd n 
1
Vout (t )  VRF  cos LO  RF  t  cos LO  RF  t
4
 2
 cos  3LO  RF  t  cos  3LO  RF  t  ......
1
6
 For LF  LO  RF &   LO  RF , Conversion loss is:
 PRFAvail   VRF   
L min
 10 log  Avail   20 log10    20 log10    3.92
  2 /   VRF 
C
 PIF  2 17/33
 Mixer Performance Measure (2/6)
Conversion Loss: SSB vs. DSB
 PRFAvail 
Lmin
C  10 log  Avail 
 PIF 

LC ,DSB
PIF , DSB  2 PIF , SSB LC ,DSB 
2

 In dB Conversion loss of DSB is 3 dB less than SSB.

 When mixer’s physical temperature is same as room temperature,
NFSSB=LC,SSB, NFDSB=LC,DSB/2

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 Mixer Performance Measure (3/6)
2. IMD: Intermodulation products:
If two closely spaced tones at ωR1 and ωR2 are applied to mixer with LO
as ωLO: (Ignoring cross product between ωR1 and ωR2 )

Upper Sidebands :
L   nR1  (n  1)R 2 
Lower Sidebands :
L   nR 2  (n  1)R1 

where, n  2,3, 4,....

Courtesy: I. Bahl et.al., Microwave Solid state circuit design, Wiley 19/33
 Mixer Performance Measure (4/6)
3. Dynamic Range and Linearity:
 The spurious free dynamic range is defined as the range from the
threshold thermal noise level upto the level at which IMD product
begin to exceed the primary response. This is called Third order
intercept point.
 Why Third order: Since they
appear as first spurious
frequencies when RF input
power is increased.
 The greater the vale of TOI point,
better the suppression of IMD3.
 Typical Value: 9-11 dB above P1
dB

Courtesy: I. Bahl et.al., Microwave Solid state circuit design, Wiley 20/33
 Mixer Performance Measure (5/6)
4. Harmonic Suppression:
 While pumping from LO, the harmonics are generated by the resistive
non-linearity.
 Power in harmonics is roughly proportional to 1/n2H, where, n is
order.
 In receiver application, it is necessary to prevent harmonics of LO
radiated into the environment through antenna.
5. Isolation:
 Isolation between mixer ports is the attenuation experienced by a
signal fed at one port and measured at another.
 LO leakage measurement is most important as LO is high power. E.g.
LO to RF isolation, LO to IF isolation etc.
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 Mixer Performance Measure (6/6)
6. RF Matching:
 The RF input VSWR expresses how well a mixer circuit is matched to
the RF source at a particular combination of ωR and PL .
 Any mismatch will add to mixer conversion loss.
 Generally, LO is high power, therefore more focus is given to the RF
matching. Matching at hyperbolic mean is in practice.
7. IF Matching:
 IF impedance is function of both PL and RF impedance.
 Poor IF match will effect conversion loss as well as noise figure of of
the following IF amplifier.

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 Mixer Design: Single Ended Mixer (1/2)
 RFC is used to bias diode.
 LO and RF isolation is decided by input combiner.
 DC return must be provided.

VDC
RFC

Coupler/ LO/RF
Combiner Matching LPF
Network DC return
LO

 Diode matching is done as hyperbolic mean of two diode states

ZON and ZOFF.

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 Mixer Design: Single Ended Mixer (2/2)
Return path for DC component of
diode current, tuning quarter-wave
stub for RF and LO frequencies, a
sum filter, lumped LPF for IF.

Courtesy: I. Bahl et.al., Microwave Solid state circuit design,

Wiley

 Image enhancement is obtained by properly positioning the image

reject filter.
 LPF to suppress SUM freq. prevents it from propagating to RF path.
24/33
 Mixer Design: Single Balanced Mixer (1/3)
 Case 1: RF voltage is applied in phase, LO is applied out of phase.

mRF  nLO

Courtesy: S.A. Maas, Microwave Mixers, Artech House

V1  VL cos Lt  VR cos R t

V2  VL cos Lt  VR cos R t
25/33
 Mixer Design: Single Balanced Mixer (2/3)
 Case 1: RF voltage is applied in phase, LO is applied out of phase.
V1  VL cos Lt  VR cos R t
V2  VL cos Lt  VR cos R t
1. All (m, n) spurious response, where m,
n are even, Eliminated.
2. Spurious response with m is even and n is odd are Eliminated.
 Case 2: LO is applied in-phase, RF is applied out of phase
V1  VL cos Lt  VR cos R t
mRF  nLO
V2  VL cos Lt  VR cos R t
1. The diodes conductance waveform are out of phase (due to
diode orientation), but RF voltage is also out of phase, so IF
current combine in phase.
2. Spurious response with m is odd and n is even are Eliminated.
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 Mixer Design: Single Balanced Mixer (3/3)

 LO voltage is applied in phase, RF is applied out of phase.

 Recoomended to put two diodes as close as possible.

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Mixer Design: Double Balanced Mixer (1/2)

 DBM can be obtained by

combining two SBMs using
180 degree hybrids.
 D1 and D2 belong to the
upper SBM and diodes D3
and D4 belongs to lower
SBM.

28/33
 Mixer Design: Double Balanced Mixer (2/2)

 All (m, n) spurious response, where (m,n) are even, Eliminated.

 Spurious response with m is even and n is odd and vice versa both
are Eliminated
 Two baluns are required.
 Higher level of LO drive required. 29/33
 Mixer Design: Image Rejection (1/4)

I1/  I m ,n   m R  n L  I 2/  I m,n   m  R  90   n L 

If θL =0 If θR =0
I1/  I m,n   m R  I1/  I m,n   0 
I 2/  I m,n   m  R  90   I 2/  I m,n   m90 

f IF  mf RF  nf L f IF ,image  m  1, n  1  f RF  f L
In Fig. 2: fR1 is RF, fR2 is Image. f IF  m  1, n  1   f RF  f L 30/33
 Mixer Design: Image Rejection (2/4)

I1/  I m,n   0  I 2/  I m,n   m90 

I1  m  1, n  1   I m,n 0  I m ,n 180   0

1
I1   I1  I 2/ 90 
1 /
2 2
I1  m  1, n  1   I m ,n 0 
1
2

I 2   I1/ 90  I 2/  I 2  m  1, n  1   I m,n 90  I m ,n 90   I m ,n 90

1 1
2 2
I 2  m  1, n  1   I m,n 90  I m ,n   90   0
1
2 31/33
 Mixer Design: Image Rejection (3/4)
Corresponds to Image
I1  m  1
I R  20 log
I1  m  1
I1/  I m,n   m R 
I 2/  I m,n   m  R  90  
I1 
1 /
2

I1 m R1  I 2/ m R 2   m  1 90
I1 (m  1) 
1 /
2
  
I1  R1  I 2/  R 2  180 
1 /
2
I1  R1  I 2/  R 2 
I1 (m  1) 
1 /
2
 
I1    R1  I 2/    R 2

If I 2/ 1 /
A ;    R 2   R1 I1 (m  1)  I1  R1 1  A 
I / 2
1 1
I1 (m  1)  I1/    R1 1  A   
2 32/33
 Mixer Design: Image Rejection (4/4)

I1  m  1 1  A
2

I R  20 log  10 log

I1  m  1 1  A  
2

I R  10 log
1  Ae j 
1  Ae  j 

1  Ae  j 
1  Ae 
j 

IR  10 log
 1  A2  A  e j  e  j  
1  A 2
 A  e j  e  j 

I R  10 log
1  A 2
 2 A cos    
1  A 2
 2 A cos    

33/33