Design of Matching Network in Microwave FET...

Design of Matching Network in Microwave FET Amplifiers

Lucio Scucchia

17th ITSS - Pforzheim 2007

Dipartimento di Ingegneria ElettronicaUniversità degli Studi di Roma “Tor Vergata”Roma - ITALY

2

IntroductionSmith Chart Impedance Transformation with LEsTransmission Lines Narrow Band Matching with LEs and TLsBroad-Band Matching with LEs and TLsMatching at 2 frequencies with LEsDC Biasing, Stability and GainDesign of a Gain Amplifier at 2 frequenciesConclusions

3

Introduction (1)

Why impedance matching ?

Maximization of the return loss for Gain Amplifier.

Minimization of the Noise Figure for Low Noise Amplifier

Maximization of the output power for Power Amplifier.

Minimization of signal distortion in transmission lines, avoiding wavefront reflections and pulse superposition.

4

To avoid unnecessary power loss, lossless matching network are considered.

The Lossless Matching Network transforms ZL into 50 Ω or 50 Ω into ZL

*.

Simple Matching Networks are usually more reliable than more complex Networks .Matching Network can be carried out with:

Matching

NetworkZL

50 Ω

Lumped Elements (LE)Transmission Lines (TL)

Introduction (2)

5

Smith Chartand

Impedance transformation with LEs

6

0

0

11

Lr i

L

ˆZ R Zj ˆZ R ZΓ Γ Γ − −

= + = =+ +

R0

ZL

+

V

-

V+

Vs

V -

I

0

0

1 1V R I2 21 1V R I2 2

V = +

jΓ Γ Γ

+

−

+ −

−

+

= ⋅ + ⋅

= ⋅ − ⋅

= + =r i

V

V

V V

VV

Incident Wave Voltage

Reflected Wave Voltage

Reflection Coefficient

One port characterization

2 r

i

PP

Γ =

Smith Chart (1)

7

The Smith Chart (SC) is a graphical tool useful to design high frequency circuits.

Every point on the SC represents a normalized impedance and the corresponding reflection coefficient.

The SC is achieved by plotting on the plane of the reflection coefficient the curves corresponding to constant resistance and reactance values.

10 1010 20 Γ= = −i

r

PRL log logP

|Γ| =1 , RL= 0 dB

No Reflection

TotalReflection

|Γ| =0 , RL= ∞ dB

Smith Chart (2)

Return Loss

8

To get curves corresponding to constant resistance values

( ) ( )2 2

2 22 2

1 1 21 1 1

r i

ˆ ˆ ˆ ˆ ˆR - jX R - X Xj jˆ ˆR jX ˆ ˆ ˆ ˆR X R XΓ Γ Γ+ + ⋅

= = + = ++ + + + + +

2 2 2 11 1r i r

ˆ ˆR Rˆ ˆR R

Γ Γ Γ⋅ −+ − ⋅ =

+ +The equation describing a circle family with parameter is achieved R

If parameteris removed

X

Z X

R

R = 0 R = 1

R = 2

Γi

Γr

Γ

1-1

1

-1

^ ^^

Smith Chart (3)

9

Z X

R

X = 0

X = 1X = 2

Γi

Γr

Γ

1

1

-1X =- 1

X = -2^ ^

^ ^

^

To get circles corresponding to constant reactance values

( ) ( )2 2

2 22 2

1 1 21 1 1

r i

ˆ ˆ ˆ ˆ ˆR - jX R - X Xj jˆ ˆR jX ˆ ˆ ˆ ˆR X R XΓ Γ Γ+ + ⋅

= = + = ++ + + + + +

2 2 22 1ir i r X

ΓΓ Γ Γ ⋅+ − ⋅ − = −

The equation describing a circle family with parameter is achievedX

If parameteris removed

R

Smith Chart (4)

10

0 0 0

0 0

0

1 11

1 1 1L L L

L L

L

ˆZ R Y G G Y YˆZ R G Y Y

Y G

Γ−

− − −= = = =

+ + ++

Placing the constant resistance circles on the constant reactance circles the SC is achieved.

Γ can be expressed as a function of the normalized admittance

So the SC of the admittance is obtained by a 180° rotation of the impedance Smith Chart

ˆ ˆR > 0 X > 0

ˆ ˆR > 0 X < 0

ˆ ˆG > 0 B < 0

ˆ ˆG > 0 B > 0

Γ Ŷ is equal to Γ -Z

Smith Chart (5)

11

Smith Chart (6)

0ZY

=∞=

ˆˆ

∞==

Z0Y

ˆˆ

1Z1Y

==

ˆˆ

( ) 2j1Zj1Y

+=−=

ˆˆ ( )

j1Z2j1Y

+=−=

ˆˆ

( ) 2j1Zj1Y

−=+=

ˆˆ ( )

j1Z2j1Y

−=+=

ˆˆ

jZjY

=−=

ˆˆ

jZjY−=

=ˆˆ

|Γ||Γ

12

Y3Y1

j [S]L

−ω

Y4Y1

j C [S]ω

Z5Z2

jC

− [Ω]ω

Z6

Z2

j L [ω Ω]

Y1

1Lω

C ω

1C

ω

Z2

Lω

Smith Chart (7)

13

Transmission Lines

14

In microwave circuits the transmission lines are fundamentally used:

• to convey high frequency signals from one point to another point.

• to obtain filters and matching networks.

GroundPlane

GroundPlane

Conductor

Ground Plane

Conductor

MicrostripLine

CoplanarWaveguide

Transmission Lines (1)

15

For the structures shown, infinitesimal line lengths can be modeled using the following network :

+

-V(z)

+

-V(z+ dz)

R dz L dz

GdzCdz

I(z) I(z + dz)

Applying Kirchhof’s voltage and current laws and solving the 2 equations obtained for an infinitesimal line length:

G (S/m)R (Ω/m)L (H/m) C (F/m)

0

1(z) = + (z) = ( - )Z

- z z - z ze e e eγ γ γ γ⋅ ⋅ ⋅ ⋅⋅ ⋅ ⋅ ⋅ ⋅+ - + -V V V I V V

+ ≅ ++ ≅ +

I( z dz ) I( z ) dI( z )V( z dz ) V( z ) dV( z )

The line length is infinitesimal so:


16


= ω L Cβ ⋅

0 00

L 1Z = YC Z

=Z0 = Characteristic impedance

β = Phase constant

To simplify the synthesis approaches the TLs used are supposed to be ideal.

( )+ - + -

0

1V(z)=V V I(z)= V VZ

- j z j z - j z j ze e e eβ β β β⋅ ⋅ ⋅ ⋅⋅ + ⋅ ⋅ ⋅ − ⋅

( )( )

L 00in

L0

Z +j ZZ ( )=

Z j Zθ

θθ

⋅⋅

+ ⋅tan

Ztan

Transmission Line Equation:

Z=0

ZLZ0 β

-l

V - j le β− ⋅

V j le β+ ⋅

= β θ⋅l = Electrical length

( )( )

L 0in 0

0 L

Y +j YY ( )=

Y j Yθ

θθ

⋅⋅

+ ⋅tan

Ytan

G=0R=0

17

YL= Y0

0

2

inL

YY

Y=

Y0 θ YL

Quarter-Wave Transformer : 2πθ =

Yin=Y02/YL

YL

Yin=YL

LinY Y=Y0 θ YL

Yin

YL

inYY0 θ YL

L0Y Y≠


18

Short-circuited stub: YL= ∞ Open-circuited stub : YL=0

θ

B

π/2θ3θ2θ1

( )0

inj YY

tan θ−=

Y0 θ( )0inY jY tan θ= ⋅

Y0 θ

θ1

θ2

θ3

θ1

θ2

θ3

θ

B

π/2θ3θ2θ1


19

Narrow Band Matching

20

2Y

1Z

Z3

With 2 lumped elements

Narrow Band Matching (1)

Z1

50 [Ω] 50[ Ω]

Y2

50 [Ω]

Z1

50 [Ω]

Y2

50 [Ω]

Z3

50 [Ω]

Z3

Z3

50[ Ω] 50 [Ω]

Z3

21


50 [Ω]Z*

Z

50 [Ω]

The same reactive network: transforms 50 Ω Ztransforms Z* 50 Ω

Z*

Z

50Ω

22


50 [Ω]Z

Z*

50 [Ω]

The same reactive network: transforms Z to 50 Ωtransforms 50 Ω to Z*

Z

Z *50Ω

23

Using a TL and a short-circuited stub

( ) ( )2 2 2 2 21 1

0.020.02L L

L

b B G Y YG

= ⋅ + + − +

( )( )

11

0.020.02

L

L L

Y GArcTan

B b Gθ

⎡ ⎤−= ⎢ ⎥

⋅ − ⋅⎣ ⎦2

2YArcTanb

θ ⎡ ⎤= ⎢ ⎥⎣ ⎦


θ1 length TL

θ 2 len

gth

stub

YA

-b

YA*

YL

YL= GL+ jBL

Y1 θ1

YC=YA+YB=0.02

YA=0.02+j b

Y2 θ2

YB=-j b

24

YL

YC=YA+YB=0.02

Y1 θ1

YA=0.02- j b

Y2 θ2YB= j b

Using a TL and an open-circuited stub

( ) ( )2 2 2 2 21 1

0.020.02L L

L

b B G Y YG

− = − ⋅ + + − +

( )( )

11

0.020.02

L

L L

Y GArcTan

B b Gθ

⎡ ⎤−= ⎢ ⎥

⋅ − ⋅⎣ ⎦2

2

bArcTanY

θ⎡ ⎤

= ⎢ ⎥⎣ ⎦

Narrow Band Matching (5)θ 1

leng

thTL

θ 2len

gth st

ub

YA

YA*

YL

25

Broadband Matching

26

Broadband Matching

In general broader bandwidth is achieved when the compensated load curve presents the maximum allowable RL at the high, low and medium frequencies.

YL(fh)

RLmax=10 dB

YIZI

YIIZII

YL(fl)YB(fh)

YB(fl)

The resulting load curve liesin a specified RL circle.

20

020

20

020

1 10 1

1 10

1 10 1

1 10

RL max

I IRL maxI

RL max

II IIRL maxII

Z R YZ

Z R YZ

−

−

−

−

−= =

+

+= =

−

Broadband Matching (1)

27

With lumped elements

1. The first two elements are selected to position the mid frequency impedance point to accept RLmax (YI-ZI or YII-ZII)

2. The other two elements form a series or shunt resonant circuit which wraps the load curve into the required RLmax circle.

YL(fh)

RLmax=10 dB

YIZI

YIIZII

YL(fl)YB(fh)

YB(fl)

2 sections are considered (4 elements).

YLZL

YAZA

SEC.2

SEC. 1

YBZB


28

YA(f)YL(f )ZA(f )ZL(f )

ZL(fm)ZL(fh)

ZL(fl)

ZA(fm) =ZII

ZA(fh)

ZA(fl)

ZI

C1

YL(fm)YL(fh) YL(fl)

YA(fh)

YA(fl)

YA(fm)=YI YII

C2


29


ZA (f) ZB(f)

ZL(fm)ZL(fh)

ZL(fl)

ZI

ZA(fh)

ZA(fl)

ZB(fh)

ZB(fl)

YL(fm)YL(fh) YL(fl)

YA(fh)

YA(fl)

Y2

ZB(fh)

ZB(fl )

YA(f) ZB(f)

30

With distributed elements

The first section is a high impedance line. It must transform the load admittance so that the resulting conductances at fl and fhare equal.TLs with high characteristic impedance allow to obtain YA with smaller susceptance at fl and fh.

3 sections are considered.

YLZL

SEC. 1

YBZB

YCZC

SEC.3

SEC.2

YAZA

YL(fh)

YL(fl)

YA(fh)

YA(fl)


31

So that the resulting admittance line is wrapped. This result is obtained using short-circuted stub. The Y2 value, fulfilling the two equations, often is too high to be realized.

YB(fh)

YB(fl)YA(fh)

YA(fl)

The TL width relative to high Y2 values is a significant fraction of λ, so the position of the line is not well defined. To reduce Y2 value :

2 2

22

tan tanl h

h

l

Y YB B ff

θ θ= − = −

Two parallel short-circuted stubParallel short and open-circuted stubs Two parallel radial stubs

The second section is a shunt element which provides positive and negative susceptance values (Bh and Bl ) at fh and fl respespectively.


32

Y1θ1

θ2

YA(f) YB(f)

Y2

θ2 Y2

YL(f) Y1 θ1

θ2a

YA(f)YB(f)

Y2

θ2b

Y2

YL(f)

Y2=0.02Sθ2a=59.2° (at 10GHz)θ2b=29.4° (at 10GHz)

Y2=0.041Sθ2=91.8° (at 10GHz)


freq (8.GHz to 12.GHz)

YA(12GHz)=0.021-j0.03

YA(8GHz)=0.021+j0.024

freq (8GHz to 12GHz)

YA(8GHz)=0.021+j0.024

YA(12GHz)=0.021-j0.03

33

The third section is a quarter wave transformer which centers the circle on the Smith Chart.To assure RL=12dB at 10GHz YII is fixed 0.0119S. YB(10GHz) is equal to 0.0592S so :

3 (10 ) 0.0265= ⋅ =II BY Y Y GHz

Y1θ1 θ2

YB(f)

Y2

θ2

Y2Yc(f)

θ1=90°(fm)

Y3

YL(f)


YII

freq (8GHz to 12GHz)

YB(10GHz) YC(f)

8.5 9.0 9.5 10.0 10.5 11.0 11.58.0 12.0

14

13

12

11

15

10

freq, GHz

RL (dB)

34

Matching at 2 frequencies with LEs

35

The matching network is composed by three sections

SECTION

3

SECTION

2

SECTION

1

YLZLY3

Z3

Y2Z2

Y1Z1

Y3(fl) = Y3(fh) =G0Z3(fl) = Z3(fh) = R0

Matching at 2 frequencies with LEs (1)

36

Four events are considered

1 1 0

1 1 0

Re[Y ( )] Re[Y ( )] > G Event A

Re[Y ( )] Re[Y ( )] < G Event B

= ⇒

= ⇒

l h

l h

f f

f f

L1 YLY1

L1 ZLZ1

1 1 0

1 1 0

Re[Z ( )] Re[Z ( )] > R Event C

Re[Z ( )] Re[Z ( )] < R Event D

= ⇒

= ⇒

l h

l h

f f

f f

00

1R = =50 ΩG

Event A Event B

SeriesInductor

G0

Event D Event C

ShuntInductor

R0

Matching at 2 frequencies with Les (2)

37

Event A Section 1

Series Inductance L1

1 1

L 1 L h 1

Re[Y ( )] Re[Y ( )]

1 1Re =Re1/Y ( ) + 2 L 1/Y ( ) + 2 L

l h

l l h

f f

f j f f j fπ π

=

⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

YL

Y1

L1 YLY1


38

If the Section 2 is a Parallel Resonant Cell

The Section 2 does not change Re[Y1]

The section 3 has to transform Re[Y1(f1)] and Re[Y1(fh)] into G0

Y2(fh)Y2(fl)

Y1(fl)

Y1(fh)

Y1

Y3(fl)=Y3(fh)=G0

YL

Y1

Re[Y1(fl)] = Re[Y1(fh)]

Event A Section 3

j X3j B3Y3 Y2

L1YLY1


39

2

2

0 33

0 33

1= + C

2 L +1 Y ( )1

= + C 2 L +1 Y ( )

G 2

G 2

l l

h h

l

h

jj f f

jj f f

f

f

π

π

π

π

⋅⋅

⋅⋅

2 10 l l

2 10

3 3

h 3 h 3

1Re[Y ( )] = Re Re[Y ( )]

1/(G - 2 C )- 2 L

1Re[Y ( )] =Re Re[Y ( )]

1/(G - 2 C )- 2 Lh h

l lj f j f

j f j f

f f

f f

π π

π π

⋅ ⋅

⋅ ⋅

⎡ ⎤=⎢ ⎥

⎣ ⎦⎡ ⎤

=⎢ ⎥⎣ ⎦

2

2

03

3

03

3

1 1= +

1 1 j 2 L + j 2 C Y ( )

1 1= +

1 1 j 2 L + j 2 C Y ( )

G

G

l l

h

h h

lff f

ff f

ππ

ππ

⋅⋅

⋅⋅

2 1

0

2

0

3 3

1

3 3

1Re[Y ( )] = Re Re[Y ( )]

1 1-

G -1/( 2 L ) 2 C

1Re[Y ( )] =Re Re[Y ( )]

1 1-

G -1/( 2 L ) 2 C

l l

h h

h h

l l

j f j f

f f

j f j f

f f

π π

π π

⋅ ⋅

⋅ ⋅

⎡ ⎤⎢ ⎥

=⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦⎡ ⎤⎢ ⎥

=⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

Event A Section 3


40

Event A Section 2

1 1

2 2

Y ( ) Y ( )

Y ( ) Y ( )

l h

l h

f f

f f

2 1 22

2 1 22

1 Im[Y ( )]-Im[Y ( )] = 2 C -

2 L1

Im[Y ( )]-Im[Y ( )] = C -2 L

2h

l l ll

h hh

f f ff

f ff

f

ππ

ππ

Section 1

Section 3

2

2

L CSection 2


41

C3

L3

Y3

Y3

YL

YL

L2

C2

Y2=G2+j B2

Y2

L1

Y1=G1+j B1

Y1

Event A


42

If the Section 2 is a Parallel Resonant Cell

The Section 2 does not change Re[Y1]

The Section 3 has to transform Re[Y1(fl)] and Re[Y1(fh)] into G0

Re[Y1(fl)] π Re[Y1(fh)]

YL

Y1

L1 Y3(fl)= Y3(fh)=G0

Y2(fh)

Y2(fl)

Y1(fl)

Y1(fh)

L3

Event B Section 1 - 3

j X3Y3 Y2

L1YLY1


43

2 1

2 1

Re[Y ( )] = Re[Y ( )] Re[Y ( )] = Re[Y ( )]

l

h h

lf ff f

1

3

L C

L 1

L 1

3

3

0

0

1 1Re = Re

1/Y ( )+ 2 L -

1 1Re = Re

1/Y ( )+ 2 L -

12 C

12 C

1G

1G

l

h h

l

h

lf j f

f j f

j f

j f

π

π

π

π

⋅

⋅

⋅

⋅

⎡ ⎤⎢ ⎥ ⎡ ⎤⎢ ⎥ ⎢ ⎥⎣ ⎦⎢ ⎥⎢ ⎥⎣ ⎦⎡ ⎤⎢ ⎥ ⎡ ⎤⎢ ⎥ ⎢ ⎥⎣ ⎦⎢ ⎥⎢ ⎥⎣ ⎦

C3

G0

L2

L1C2

YL

Y1=G1+j B1Y2=G2+j B2

3 L 1

3 L 1

0

0

1 1Re = Re

1/G - 2 L 1/Y ( )+ 2 L

1 1Re = Re

1/G - 2 L 1/Y ( )+ 2 L

l l l

h hh

j f f j f

j f f j f

π π

π π

⋅ ⋅

⋅ ⋅

⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

1

3

L L

L3

G0

L2

L1C2

YL

Y1=G1+j B1Y2=G2+j B2

Event B Section 1 - 3


44

Event C

ZL

ZL

Z1

L1

Z1=R1+j X1

Z2

L2C2

Z2=R2+j X2

C3

L3

Z3

Z3


45

DC Biasing, Stability and Gain

46

To get the required perfomances the biasing point has to be selected

DC Block

DC Block

VDD

VGG

To analyse stability and gain of a small-signal amplifier the transistor and the biasing networks can be represented by S-parameters.

(S11, S12, S21, S22)

Idss

0.9 Idss

Ids(mA)

0.15 Idss

0.5 Idss

3 6 9Vds( V )

Vgs= 0V

Vgs= -2V

Vgs= -3V

Vgs= -4V

Vgs= -1V GAIN

LINEARITY

NOISE

DC Biasing, Stability and Gain (1)

47

Uncoditionallystable

12 2111

22

12 2122

11

1

1

Lin

L

Sout

S

s sss

s sss

ΓΓΓ

ΓΓΓ

⋅ ⋅= +− ⋅

⋅ ⋅= +− ⋅

( ) 1 ( ) 1in L out S&Γ Γ Γ Γ< <

for (|ΓS| <1 & |ΓL|<1 )

ΓS Plane ΓL PlaneZS ZL

Zin= ZS* Zout= ZL

*

Simultaneous Conjugate matching


R0

ZoutΓout

Outputnetwork

ZSΓS

ZLΓL

Inputnetwork

ZinΓin

VS

R0

49

The stability can be studied only on the GS plane if the condition Zout =ZL

* is realized.

The MSG Circle has to be defined.

The stability is guaranteed if ZS is chosen outside the MSG circle.

The device is unconditionally stable if :

2 2 211 22

12 21

11 22 12 21

11

2

1

k Rollet Stability Factor' s

S SS S

S S S S

Δ

Δ

= =

− − += >

⋅

= ⋅ − ⋅ <

|Γin|=1ΓL Plane

ZL

Zout = ZL*

|Γout|=1ΓS Plane

MSGCircle

ZS

Zinπ ZS*


50

If Simultaneous Conjugate Matching (S.C.M.) is verified the Gains are maximized and GTmax= GAmax = G max= MAG

If the System is conditonally stable the S.C.M. is not possible and a set of couples (Zs , ZL) provide the obtainable GTmax= GAmax = G max= MSG

2112

SMSG

S=

( )2211

12S

MAG k kS

= ± −

( , , )

( , )

( , )

LT S L

As

AoA S

As

LL

in

PG GP

PG GP

PG GP

Γ Γ

Γ

Γ

= =

= =

= =

S

S

SPAo

Outputnetwork

PL

R0

PAs

Inputnetwork

Pin

VS

R0


51

Unconditionally Stable Device

ΓS PlaneGA = MAGGA1< MAGGA2 < GA1GA3 < GA2GA4 < GA3

ZS

Conditionally Stable Device

ΓS Plane

GA = MSGGA1< MSGGA2 < GA1GA3 < GA2


52

Design of a Gain Amplifier at 2 frequencies

53

Design Procedure at a Given Frequency

1) Choice of the device2) Biasing network design3) Stability condition 4) Choice of Zs5) Input Network Design6) Computation of Zout

7) Output Network Design

Inputnetwork

R0OutputnetworkVS

R0

ZSMSG Zout

SC

ZL= Zout*Zin

Design of a Gain Amplifier at 2 frequencies (1)

54

The matching technique described can be used considering 2 frequencies. The used device is a low-noise GaAs FET with a 4x50μm gate periphery by Alenia. The operating frequency is 5 GHz (fl = 4 GHz, fh = 6 GHz ).

Choice of ZS(fl) and ZS(fh) so that GA(fl) = GA(fh) and stability condition is satisfied.Imput Network design.Computation of Zout (fl) and Zout (fh).Output network design for the conjugate matching.

ZS(fl)(

ZS(fh)(

Zin(fl) (Zin(fh)

Zout(fl) (Zout(fh)

(


55

R0Inputnetwork

OutputnetworkVs

R0

3.6 nH

1.6 n F

1.1 pF

0.2 p F

V ggV dd

0.5 pF

0.2 pF

5.8 nH

2.3 nH

Matching network element values

C2: MICAP3W=10 mmL=10 mmGe=10 mmL=10 mmNP=2Wt=20mmWF=20mm

InputNetwork

L1: MRIND N=2.25L1=200 mmL2=224 mmW=10 mmL=10 mm

L2: MRINDN=3.25L1=280 mmL2=305 mmW=10 mmL=10 mm

C3: TFC W=61mmL=74mmT=0.3mmEr=7.8DO=10mm

Output Network



C2: TFC W=49 mmL=49 mmT=0.3 mmEr=7.8DO=10 mm

C3: TFC W=61 mmL=68 mmT=0.3 mmEr=7.8DO=10mm


56

1 2 3 4 5 6 7 8 9 10

freq, GHz

-20

-16

-12

-8

-4

0|S(2,2)| [dB]

MMIC

lumped

1 2 3 4 5 6 7 8 9 10

freq, GHz

0

4

8

|S(2,1)| [dB]

12

16

MMIC

lumped


57

Conclusions

Some fundamental points about matching have been examined.

A systematic approach for matching network design has been described.

In order to demonstrate the usefulness of the proposed approaches a gain amplifier design has been carried out.

Design of Matching Network in Microwave FET...

Documents

Transcript of Design of Matching Network in Microwave FET...