Chapter 4 passive components

gioi thieu transistor

Chapter 4 Passive Components

Chapter 4 Passive Components

® # Circulators Pozar, Ch9 Ferrimagnetic Components)

® for ideal circulators (all matched & no insertion loss)

S51, =S32 =1=> signal flowing I->2 & 2->3 S;=l = signal flowing 2-1@1-3

$3, =S23=0 > nosignal flowing 1>3 & 32

%as=0 =nosignal flowmg 2-3

Clockwise circulator Counterclockwise circulator

3-port microwave circulator

(Ix- & Rx-port isolation Š:¡ is important for receiving)

@ Resistive Divider ( Matched, Reciprocal, not lossless )

If a three-port divider contains lossy components it can be made to be matched

at all ports using lumped element resistors

All ports are matched due to symmetry: 5S); = S22 = $33 =0

=> insertion loss UL) = — I0ls| 2+ |- -10la| 5

in

@® Wilkinson Power Divider

( Matched, reciprocal, not lossless for power combining )

(b) Microstrip ling realization

Si) Sp Sa 0 — j0.707 — 70.707 [S]=| S21 So2 S23 |=} — 70.707 0 0

S3,; S35 S33} |—j0.707 0 0

=> S11 = 5522 = S33 =0 : all three ports matched

Comparison between Resistive Divider & Wilkinson Power Divider

Matched at all ports Matched at all ports

No isolation between ports Isolation between Port-2 & port-3

Comparison between Resistive Divider & Wilkinson Power Divider

not high frequency

@® 1.6-GHz Wilkinson Power Divider

Mạch ghép chia công suất wilkinson

® Four-porf netfwork : directional couplers, hybrids,

For a reeiprocal four-port network matched at all ports [S] =| |

= a measure of the coupler's ability to isolate forward wave (to port 3)

and backward wave (to port 4)

= a measure of the coupler's ability to isolate input port 1& port 4

Example 4.1 A 10-dB directional coupler has a directivity of 40 dB If the input power ¡ = 10 mW, what are the power outputs at ports 2, 3, and 4? Assume that the

coupler (a) is lossless and (b) has an insertion of 0.5 dB

FIGURE 4.3 Directional coupler

Solution (a) For a lossless case, C (dB) = 10 dB = 10 log(P,/P3;) = P, (dB) —

P; (dB):

P, = 10 mW = 10 dBm P; =P, —C= 10 dBm — 10 dB = 0 dBm = 1 mW

(b) For the insertion loss of 0.5 dB, let us assume that this insertion loss is equal

for all three ports:

Insertion loss = IL = x, = 0.5 dB

P, = 0 dBm — 0.5 dB = —0.5 dBm = 0.89 mW

P, = —40 dBm — 0.5 dB = —40.5 dBm = 0.000089 mW

P, = 9.5 dBm — 0.5 dB = 9 dBm = 7.9 mW a

® Quadrature ( 90° ) Hybrid (Directional Coupler)

equally combining from port - 1 & 4

to port-2 with 90° phase difference

® Port 2 & 3 outputs have 90° phase difference

@ Any port can be used as an input & output ports

will be on the opposite side of the junction

2.4GHz Branch-Line Coupler

EMLAB E.E NCKU

@® 180° Hybrid (Directional Coupler)

The 180° hybrid is a four-port network with a 180*%phase shift or in-phase between two-output ports

31 512 513 514 0 I1 1 0 [s]= %2 222 532; 5324| —/|l 0 0 -I

S}4 =0 no power flowing to port 1

port 2 & 3 combined in phase

Vig = SyVq + S433 + Sah = : (-V, + V3)

port 2 & 3 combined in 180° phase difference

180° Ring Hybrid (or Rat-Race Hybrid)

Example

180° ring hybrid for differential CMOS LNA measrement: fg = 5.7 GHz , FR-4:

e, = 4.7,d=1 mm

*Che-Hong Liao and Huey-Ru Chuang

“A 5.7GHz 0.18-m m CMOS Gain-Controlled Differential LNA

with Current Reuse for WLAN Receiver.” IEEE Microwave &

Wireless Component Letter, vo 13, no.12, pp.526-528, Dec 2003

2011-12

Ring coupler 180° 180° Ring coupler EMcom LAB

(as Balun) (as Balun)

Design a 180° ring hybrid for a 50 O system impedance, and plot the magnitude of the

S parameter (S;;) from 0.5/9 to 1.5 fo where fo is the design frequency

*Che-Hong Liao and Huey-Ru Chuang

“A 5.7GHz 0.18-m m CMOS Gain-Controlled Differential LNA

with Current Reuse for WLAN Receiver.” IEEE Microwave &

Wireless Component Letter, vo 13, no.12 pp.526-528, Dec 2003

_} — Couped Line Directional Coupler (Pozar P:;;)

® When two unshielded transmission lines are close together, power can be

coupled between lines due to EM fields interaction of each line

e The coupling factor & impedance matching will depend on line spacing (S),

line length (J) & line width (W)

Example Single-section strip-line coupler design

Design a 20 dB single-section coupled line coupler in stripline with a 0.158 cm esround plane spacing, dielectric constant of 2.56 , a characteristic impedance of

50 Q , and a center frequency of 3 GHz

Hence, Lange coupler in the following section should be used for tight-coupling

coupler

Photograph of a single-section microstrip coupled line coupler

_Ì The Lange Coupler ( Tight-coupling 90°-type Coupler)

@ Since the coupled line coupler is too loose to achieve 3dB or 6 dB coupling,

The Lange coupler with several lines parallel to each other can easily achieve 3dB coupling

Improves the bandwidth through compensate unequal even- & odd -mode phase velocity

A type of quadrate (90°) coupler since output ports (2 & 3 ) have a 90° phase difference Disadvantage: the lines are very narrow & close together and also it is difficult to fabricate the bonding wires across the lines

Even/odd mode characteristic impedances of the Lange coupler in terms of that of a two- conductor line are identical to any pair of adjacent lines in the coupler:

(Zoe -Z0o ) : 2 -conductor line even-/odd-mode characteristic impedances

(Z 04 -Zo 4) : 4-conductor line even-/odd-mode characteristic impedances

EXAMPLE 8.9 C /s# @ditiy )

Design a 3 dB SOQ Lange coupler for operation at 5 GHz If the coupler is to be

fabricated in microstrip on an alumina substrate with c, = 10 and d= 1.0mm,

+

compute Zo, and Zo, for two adjacent lines, and find the necessary spacing and

widths of the lines

Solution For a 3 dB coupler the voltage coupling coefficient is

C= 107*/?9 = 0.707,

so from (8.100) the even- and odd-mode characteristic impedances of a pair of

adjacent coupled lines is