Microwave Power Combiners
Power Combining
Applications of Power Combining
Power Combining Problem for Microwave PAs
Combining power from various unit PAs is one of the central
problems of high power PA design.
CMOS microprocessors have >100M transistors. Can you
produce 1uW from each of 100M small PAs and combine
them to get 100W?
Solving the power combining problem gives a solution to the
impedance matching problem - and viceversa.
Both lead to losses and bandwidth limitations
The power combining problem is related also to the problem of
separating common-mode from differential signals.
More Power Combiners
Coax Baluns
Free-space
Power Combining
Analysis Techniques for Combiners
Generally can use Z matrix, Y matrix or S matrix
Passive combiners have reciprocal matrices
Zij=Zji, Yij=Yji, Sij=Sji
Analysis is often easier by considering even or odd mode inputs
replace V1, V2 with Ve=1/2(V1+V2), Vo=1/2(V1-V2)
Even mode = common mode
odd mode voltage=1/2 differential voltage
V1
V2
V3
Ve Vo
+ -+ V1
=>
V2 + - - +
V3
Power Combiners are Frustrating
+
Simple “summer” for powers from 2 sources
which is lossless and has fixed input
impedance for both channels
Does not exist !!!
However,
Voltage summers exist
Current summers exist
Lossy power combiners exist
“Loss-less” power combiners for different frequencies exist
“Loss-less” power combiners for identical signals exist
Why Can’t You Make A Perfect Power Summer?
“A 3-port that is matched at all ports, loss-less
and made with reciprocal elements cannot exist”.
Sii=0
2
1
S
Sij=Sji
3
SjkSkn*=djn
0
1/√2eja1
1/√2eja1 0
1/√2eja2 1/√2eja3
1/√2eja2
1/√2eja3
0
]
Does not satisfy
S31 S12*+S32 S22*+S33 S32*=0
]
Wilkinson Combiner
2
1
l/4
Z=sqrt2 Zo
Sii=0
Sij=Sji
3
SjkSkn*=djn
R=2Zo
0
1/√2eja1
1/√2eja1 0
1/√2eja1 0
1/√2eja1
0
0
]
Does satisfy
S31 S12*+S32 S22*+S33 S32*=0
]
Power Combiners are Frustrating (2)
•Combiners that provide isolation between input ports
are intrinsically lossy!
loss shows up if input signals are different
•Combiners that are lossless don't provide isolation
between ports
so some power (generally difference signal)
gets reflected to the inputs, doesn't reach
output
=> You can only efficiently combine signals that
are exactly identical (or scaled in complex
amplitude)
Power Combiners Can Be Used in Very
Creative Ways
•Combiners that are lossless don't provide isolation
between ports
=> You can only efficiently combine signals that
are exactly identical (or scaled in complex
amplitude)
When you combine signals that are scaled in
complex amplitude with a lossless combiner,
You are doing active
load pulling
This is the basis for Doherty and Outphasing amplifiers
Current Summing
Simplest power combiner
Used with most transistor units
V1=V2=V3
I1+I2+I3=0
1
3
RL
2
Odd mode signals see Zodd=0 (short)
Even mode signals see Zeven= 2RL
No port-to-port isolation
Not matched to 50 ohms
Z,Y matrices don't exist
Very broadband
Can use this to combine
current sources
Or voltage sources that are
equal
Ve=1/2(V1+V2)
Vo=1/2(V1-V2)
Ie=1/2(I1+I2)
Io=1/2(I1-I2)
Current Summing
1
S parameter analysis
-1/3 2/3 2/3
b1
b2 = 2/3 -1/3 2/3
b3
2/3 2/3 -1/3
3
a1
a2
a3
2
T
Define ae=1/sqrt2 (a1+a2)
ao=1/sqrt2 (a1-a2)
be
bo
b3
=TS
T-1=T
T-1
ae
ao
a3
ae 1/sqrt2 1/sqrt2 0 a1
ao = 1/sqrt2 -1/sqrt2 0 a2
a3 0
0
1 a3
be
bo
b3
=
1/3 0 sqrt(8)/3 ae
ao
0
-1
0
a3
sqrt(8)/3 0 -1/3
ADS Modeling of Even, Odd Mode Impedance
(current summing)
combiner
freq
S(1,1)
S(2,1)
S(3,1)
1.000 GHz
0.333 / 1...
0.667 / 0...
0.667 / 0...
freq
S(4,4)
S(5,5)
S(6,4)
S(6,5)
1.000 ...
0.333 ...
1.000 ...
0.943 ...
0.000 ...
Eqn Zine=50*(1+S(4,4))/(1-S(4,4))
Eqn Zino=50*(1+S(5,5))/(1-S(5,5))
Eqn Zin=stoz(S)
freq
1.000 GHz
freq
1.000 GHz
Zineven
Zinodd
Zine
Zino
100.000 / 0.000
1.388E-14 / 0....
Zin(4,4)
Zin(5,5)
2.123E17 / 0....
1.421E-14 / 0....
Not what you want
Lossless Combiner with Z Transformation
1
Widely used inside of
high frequency ICs
l/4
Z=sqrt2 Zo
3
2
Odd mode signals see Zodd=open
Even mode signals see Zeven=RL (=Zo)
No port-to-port isolation
Not matched to 50 ohms
Limited bandwidth
Can use this to combine
voltage sources
Or current sources that are
equal
Corporate combiner (non-isolated)
l/4
Z=sqrt2 Zo
T.L.
l/4
Z=sqrt2 Zo
2 in
Parallel
l/4
Z=sqrt2 Zo
Effect of each stage
Wilkinson Combiner
1
l/4
Z=sqrt2 Zo
Widely used in circuit
boards and systems
3
2
R=2Zo
Odd mode signals see Zodd= 50 ohms
Even mode signals see Zeven=RL (=Zo)
Ports are isolated!
Matched to 50 ohms!
Limited bandwidth
Can use this to combine
voltage or current sources
Get loss to the extent that
the sources are not equal
Even & Odd Mode Analysis
Wilkinson Combiner (or Divider)
Odd
Mode
Short at
symmetry
plane
Even
Mode
Open at
symmetry
plane
Wilkinson Combiner
m1
freq=1.000GHz
S(4,4)=1.510E-4 / -180.000
impedance = Z0 * (1.000 - j4.330E-17)
m2
freq=1.000GHz
S(5,5)=2.165E-17 / 90.000
impedance = Z0 * (1.000 + j4.330E-17)
0.0
S(6,5)
S(6,4)
S(5,5)
S(4,4)
-0.1
dB(S(6,4))
-0.2
m2
m1
-0.3
-0.4
-0.5
-0.6
0.0
0.2
0.4
0.6
0.8
1.0
freq, GHz
1.2
1.4
1.6
1.8
2.0
freq (100.0MHz to 2.000GHz)
More Combiner Possibilities
Most matching structures can become combiners
m2
freq=1.000GHz
S(2,2)=1.000 / -96.478
impedance = Z0 * (-1.611E-12 - j0.893)
S(2,2)
S(1,1)
m1
freq=900.0MHz
S(1,1)=0.006 / 45.165
impedance = Z0 * (1.008 + j0.008)
0.0
m1
dB(S(3,1))
-0.2
-0.4
m2
-0.6
freq (100.0MHz to 2.000GHz)
-0.8
-1.0
0.0
0.2
0.4
0.6
0.8
1.0
freq, GHz
1.2
1.4
1.6
1.8
2.0
More Combiner Possibilities
Most matching structures can become combiners
m2
freq=1.000GHz
S(2,2)=1.000 / 78.143
impedance = Z0 * (-2.256E-12 + j1.232)
m1
freq=800.0MHz
S(1,1)=0.008 / -72.429
impedance = Z0 * (1.005 - j0.015)
m2
0.0
dB(S(3,1))
S(2,2)
S(1,1)
-0.2
m1
-0.4
-0.6
-0.8
freq (100.0MHz to 2.000GHz)
-1.0
0.0
0.2
0.4
0.6
0.8
1.0
freq, GHz
1.2
1.4
1.6
1.8
2.0
Load Pulling Effect of Combiners
Source 1
Current summing
combiner provides load
pull for current sources
Source 2=a Source1
Impedance Seen By Source 1
Z1=V1/I1
300
Assumes
source 2 is
coherent
with source 1
mag(Z1)
250
200
150
100
50
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
a
Current multiplier
Load Pulling Effect of Combiners
Source 1
Summing with l/4 lines
provides load pull for
voltage sources
Source 2=a Source1
Impedance Seen By Source 1
50
mag(Z1)
40
Assumes
source 2 is
coherent with
source 1
30
20
10
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
a
Voltage multiplier
Load Pulling Effect of Combiners
Source 1
Source 2=a Source1
Impedance Seen By Source 1
80
60
imag(Z1)
real(Z1)
40
20
0
-20
-40
-60
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
a
Voltage multiplier
4.0
4.5
5.0
General 4 Ports
With Matched Inputs & 2 Isolated Ports
(assuming lossless reciprocal components)
Not
Physically
Symmetric
Physically
Symmetric
Customary Embodiment of Coupled Line Coupler
Baluns
Balun
Differential
amplifier
+ +
- -
Balun
Key Issue In Balun
1
2
3
Equality of forward and
reverse currents
must be enforced
Broadband Coax Balun Using Ferrites
Good for low frequencies (to ~ 1GHz)
Coaxial Balun
infinite
ADS Simulation Coaxial "Balun"
Matched for odd mode input
Open for even mode input
Matched for single-ended output
ADS has a variety of transmission line models
Care must be exercised in describing T.L. baluns!
Assumes grounds
Allows ground to
be assigned but
does not consider
coupling of outer
conductor to
external elements
Can describe T.L.
balun
Want Ze=> infinity
Zo=>50 ohms
Balun-like Structures Can Be Impedance Transformers
If one can enforce If=Ir
I1
If
Ir
I2
I1=If+Ir=2 If
I2= If = I1/2
V2= 2 V1
1:4 Z transformation
If
2I
I1=If+Ir=3 If
I2= If = I1/3
V2= 3 V1
1:9 Z transformation
Other Balun Designs
5) Transformer baluns
Transformers
For ideal transformer
with 2 windings
Transformers (2)
L1-M
L2-M
M
It is somewhat difficult to show
the equivalence of these models!
Detailed Models of Transformer
(1-k2)L1
K:1
Leakage inductance
Magnetizing
inductance
Ideal transformer
k2L1
K>0.95 for low frequency with ferrite core
K~0.5-0.8 for IC layout
Zload
K=0.99999
Pretty good transformer balun
Zdiffin~50ohms
K=0.6
Not so good transformer balun
Zdiffin~30ohms + 14 nH
Integrated Transformers for PAs
Advantages
Provides impedance matching
Combines power of multiple unit PAs
DC isolation of primary/secondary
Primary inductance can be used in
matching transistor Cout
With IC process can achieve
excellent control and matching
Low cost
Disadvantages
Resistive & substrate losses
BW limitations
Die area
Different Methods of Combining
I2
I1a
I1b
I1c
Transformers in “series”
For equal turns
I1a=I1b=I1c… = I2
V1a+V1b+V1c… = V2
Transformers in “parallel”
For equal turns
I1a+I1b+I1c … = I2
V1a=V1b=V1c… = V2
An et al JSSC 43, 1064 (2008)
Integrated Transformers for CMOS PAs
Power combining ratio (serial)
Efficiency (serial)
CMOS layout
An et al JSSC 43, 1064 (2008)
Simple Integrated Balun - Transformer Based
Secondary
windings 2x as
many as for each
primary
Leakage inductance
Magnetizing
inductance
Ideal transformer
Zcom
Zload
Ideally Zdiffin = ZL/2 but have added inductance in series and in shunt
Balun Characterization
Common mode input
Differential
mode input
balun
Push-Pull Amplifier
Classic amplifier for audio applications
Combine two Class B amplifiers to get linear output
Vce
Vrf
Vo
time
match
IC1
Irf
Iave
IC2
Iave
Vo
time
RL
Irf
time
hmax=p/4*(Vmax-Vmin)/(Vmax+Vmin)
match
Can put in
harmonic tuning
here
Benefits of Push-Pull Amplifier
•Gets rid of even harmonics
can be used for very wide bandwidths (more than x2)
in situations where filtering cannot be done
•Push pull leads to more uniform current draw from supply,
so grounding source is not a big problem
•The output voltage swing is double that for a single transistor
=> higher output impedance
Drawbacks
Need for balun: potentially lossy and bandwidth limiting
Push-pull suffers same IM3 distortion as single Class B!
Perfect Class B does not generate IM3
but low gm at low bias causes problems in real life
If both transistors “on” at same time, get cross-over distortion
Balanced Amplifiers
Commonly used arrangement with 2 amplifiers fed by signals coming
from a 90o splitter (ie Lange coupler)
90 degree
hybrid
90 degree
hybrid
j
j
j
j
Benefits of Balanced Amplifiers
90 degree
hybrid
90 degree
hybrid
•Output power x2 higher
•IP3 x2 higher
•Gain the same
•Input and output match for combo much
better than for individual elements
• Output is less sensitive to impedance
mismatch of load
Effects of Amplitude and Phase Mismatch
a1
b3
a2
Would like r=1, q=0
Combining loss (dB)
0
-0.1
-0.2
-0.3
r=1
-0.4
-0.5
r=1.2
-0.6
-0.7
0
10
20
30
Angle of mismatch (degrees)
40
50
Effects of Amplitude and Phase Mismatch (2)
Consider case of power subtraction (to cancel nonlinearity)
0
Combining loss (dB)
-5
-10
-15
r=1.2
-20
-25
-30
-35
-40
r=1
-45
-50
0
2
4
6
8
Angle of mismatch (degrees)
10
12