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.

The power combining problem is related also to the problem of

separating common-mode from differential signals.

Both lead to losses and bandwidth limitations

Coax Baluns Free-space

Power Combining

More Power Combiners

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 =>

V1

V2 V3

Vo Ve

+ -

+ - - +

+ -

+

Simple “summer” for powers from 2 sources

which is lossless and has fixed input

impedance for both channels

Does not exist !!!

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

However,

Power Combiners are Frustrating

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”.

1

2

3 S

0 1/√2eja1 1/√2eja2

1/√2eja1 0 1/√2eja3

1/√2eja2 1/√2eja3 0

Sij=Sji

Sii=0

SjkSkn*=djn

] Does not satisfy

S31 S12*+S32 S22*+S33 S32*=0

]

Wilkinson Combiner

0 1/√2eja1 1/√2eja1

1/√2eja1 0 0

1/√2eja1 0 0

Sij=Sji

Sii=0

SjkSkn*=djn

] Does satisfy

S31 S12*+S32 S22*+S33 S32*=0

] 2

3

1 l/4

Z=sqrt2 Zo

R=2Zo

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

1

2

3

V1=V2=V3

I1+I2+I3=0

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

RL

Ve=1/2(V1+V2)

Vo=1/2(V1-V2) Ie=1/2(I1+I2)

Io=1/2(I1-I2)

Current Summing

S parameter analysis 1

2

3 b1

b2

b3

-1/3 2/3 2/3

2/3 -1/3 2/3

2/3 2/3 -1/3

a1

a2

a3

Define ae=1/sqrt2 (a1+a2)

ao=1/sqrt2 (a1-a2)

T

be

bo

b3

= T S T-1 ae

ao

a3

=

1/sqrt2 1/sqrt2 0

1/sqrt2 -1/sqrt2 0

0 0 1

ae

ao

a3

a1

a2

a3

=

T-1=T

be

bo

b3 =

ae

ao

a3

1/3 0 sqrt(8)/3

0 -1 0

sqrt(8)/3 0 -1/3

freq

1.000 GHz

S(1,1)

0.333 / 1...

S(2,1)

0.667 / 0...

S(3,1)

0.667 / 0...

freq

1.000 ...

S(4,4)

0.333 ...

S(5,5)

1.000 ...

S(6,4)

0.943 ...

S(6,5)

0.000 ...

Eqn Zin=stoz(S)freq

1.000 GHz

Zin(4,4)

2.123E17 / 0....

Zin(5,5)

1.421E-14 / 0....

Eqn Zine=50*(1+S(4,4))/(1-S(4,4))

Eqn Zino=50*(1+S(5,5))/(1-S(5,5))

freq

1.000 GHz

Zine

100.000 / 0.000

Zino

1.388E-14 / 0....

ADS Modeling of Even, Odd Mode Impedance

(current summing)

Zineven

Zinodd

combiner

Not what you want

Lossless Combiner with Z Transformation

Widely used inside of

high frequency ICs

1

2

3

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

l/4

Z=sqrt2 Zo

l/4

Z=sqrt2 Zo

l/4

Z=sqrt2 Zo

l/4

Z=sqrt2 Zo

Corporate combiner (non-isolated)

Effect of each stage

T.L.

2 in

Parallel

Wilkinson Combiner

Widely used in circuit

boards and systems

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

1

2

3 l/4

Z=sqrt2 Zo

R=2Zo

Even & Odd Mode Analysis

Wilkinson Combiner (or Divider)

Short at

symmetry

plane

Open at

symmetry

plane

Odd

Mode

Even

Mode

freq (100.0MHz to 2.000GHz)

S(4

,4)

1.000E91.510E-4 / -180.000

m1

S(5

,5)

Readout

m2

S(6

,4)

S(6

,5)

m1freq=S(4,4)=1.510E-4 / -180.000impedance = Z0 * (1.000 - j4.330E-17)

1.000GHz

m2freq=S(5,5)=2.165E-17 / 90.000impedance = Z0 * (1.000 + j4.330E-17)

1.000GHz

Wilkinson Combiner

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.80.0 2.0

-0.5

-0.4

-0.3

-0.2

-0.1

-0.6

0.0

freq, GHz

dB

(S(6

,4))

m1freq=S(1,1)=0.006 / 45.165impedance = Z0 * (1.008 + j0.008)

900.0MHz

m2freq=S(2,2)=1.000 / -96.478impedance = Z0 * (-1.611E-12 - j0.893)

1.000GHz

freq (100.0MHz to 2.000GHz)

S(1

,1)

9.000E80.006 / 45.165

m1

S(2

,2)

1.000E91.000 / -96.478

m2

m1freq=S(1,1)=0.006 / 45.165impedance = Z0 * (1.008 + j0.008)

900.0MHz

m2freq=S(2,2)=1.000 / -96.478impedance = Z0 * (-1.611E-12 - j0.893)

1.000GHz

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.80.0 2.0

-0.8

-0.6

-0.4

-0.2

-1.0

0.0

freq, GHz

dB

(S(3

,1))

More Combiner Possibilities Most matching structures can become combiners

m1freq=S(1,1)=0.008 / -72.429impedance = Z0 * (1.005 - j0.015)

800.0MHz

m2freq=S(2,2)=1.000 / 78.143impedance = Z0 * (-2.256E-12 + j1.232)

1.000GHz

freq (100.0MHz to 2.000GHz)S

(1,1

)

8.000E80.070 / -39.239

m1

S(2

,2)

1.000E91.000 / 83.531

m2

m1freq=S(1,1)=0.008 / -72.429impedance = Z0 * (1.005 - j0.015)

800.0MHz

m2freq=S(2,2)=1.000 / 78.143impedance = Z0 * (-2.256E-12 + j1.232)

1.000GHz

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.80.0 2.0

-0.8

-0.6

-0.4

-0.2

-1.0

0.0

freq, GHz

dB

(S(3

,1))

More Combiner Possibilities Most matching structures can become combiners

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.50.0 5.0

100

150

200

250

50

300

a

ma

g(Z

1)

Impedance Seen By Source 1

Z1=V1/I1

Source 1

Source 2=a Source1

Current multiplier

Load Pulling Effect of Combiners

Current summing

combiner provides load

pull for current sources

Assumes

source 2 is

coherent

with source 1

Impedance Seen By Source 1

Source 1

Source 2=a Source1

Voltage multiplier

Load Pulling Effect of Combiners

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.50.0 5.0

10

20

30

40

0

50

a

mag(Z

1)

Summing with l/4 lines

provides load pull for

voltage sources

Assumes

source 2 is

coherent with

source 1

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.50.0 5.0

-40

-20

0

20

40

60

-60

80

a

rea

l(Z

1)

ima

g(Z

1)

Source 1

Source 2=a Source1

Load Pulling Effect of Combiners

Impedance Seen By Source 1

Voltage multiplier

General 4 Ports

With Matched Inputs & 2 Isolated Ports

(assuming lossless reciprocal components)

Not

Physically

Symmetric

Physically

Symmetric

Customary Embodiment of Coupled Line Coupler

+

-

+

-

Differential

amplifier Balun Balun

Baluns

Key Issue In Balun

Equality of forward and

reverse currents

must be enforced

1 2

3

Broadband Coax Balun Using Ferrites

Good for low frequencies (to ~ 1GHz)

infinite

Coaxial Balun

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

1:4 Z transformation

2I

Balun-like Structures Can Be Impedance Transformers

If one can enforce If=Ir

I1 If I2 I1=If+Ir=2 If

I2= If = I1/2

V2= 2 V1 Ir

I1=If+Ir=3 If

I2= If = I1/3

V2= 3 V1

1:9 Z transformation

If

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!

Ideal transformer

Zload

Leakage inductance

Magnetizing

inductance

Detailed Models of Transformer

(1-k2)L1

k2L1

K:1

K>0.95 for low frequency with ferrite core

K~0.5-0.8 for IC layout

Pretty good transformer balun

Zdiffin~50ohms

Not so good transformer balun

Zdiffin~30ohms + 14 nH

K=0.99999

K=0.6

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

Transformers in “series” I1a

I1b

I1c

I2

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

Different Methods of Combining

An et al JSSC 43, 1064 (2008)

Integrated Transformers for CMOS PAs

An et al JSSC 43, 1064 (2008)

Power combining ratio (serial)

Efficiency (serial)

CMOS layout

Simple Integrated Balun - Transformer Based

Secondary

windings 2x as

many as for each

primary

Ideal transformer

Zload Zcom

Leakage inductance

Magnetizing

inductance

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

hmax=p/4*(Vmax-Vmin)/(Vmax+Vmin)

time

time

Vo

Vce

Iave

IC1

Vrf

Irf

Classic amplifier for audio applications

Combine two Class B amplifiers to get linear output

time Iave

IC2

Irf

match

Vo RL

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

•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

Benefits of Balanced Amplifiers

90 degree

hybrid 90 degree

hybrid

Effects of Amplitude and Phase Mismatch

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0 10 20 30 40 50

Angle of mismatch (degrees)

Co

mb

inin

g l

oss

(dB

)

r=1

r=1.2

a1

a2

b3

Would like r=1, q=0

Effects of Amplitude and Phase Mismatch (2)

Consider case of power subtraction (to cancel nonlinearity)

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

0 2 4 6 8 10 12

Angle of mismatch (degrees)

Co

mb

inin

g l

oss

(d

B)

r=1

r=1.2