lect121222

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ELEC344, Kevin Chen, HKUST 1

Why impedance matching?

Maximum power is delivered when the load is matched to

the line.

Impedance matching sensitive receiver components

(antenna, LNA, etc.) improves the signal-to-noise ratio ofthe system.

Impedance matching in a power distribution network (such

as antenna array feed network) will reduce amplitude and

phase errors.

Impedance matching uniquely removes the requirement for

a specific reference plane.

Provide reliable and predictable interconnections betweencomponents in a system.

Lect. 12: Impedance Matching


Load

ZL

Matching

networkZ0

A lossless network matching an arbitrary load impedance to a

transmission line

Complexity --- Simplest design that satisfies the required

specification is generally the most preferable. Cheaper,

more reliable, less lossy.

Bandwidth --- Normally, it is desirable to match a load over

a band of frequencies. Increased bandwidth usually comes

with increased complexity, e.g. using multistage matching.

Design issues of the matching networksMultiple solutions


Implementation --- Choose the right type of matching

networks, either tuning stub or transmission line.

Adjustability --- This maybe required for applications where a

variable load impedance occurs.

Matching with Lumped Elements (L Networks)

Network for zL inside the

1+jx circle (smith chart).

Network for zL outside the

1+jx circle (smith chart).


L networks consist of two reactive components (inductor and

capacitor), which results in eight different configurations.

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Analytic solution for the matching network elements

Case 1: load impedance inside the 1+jx circle --->RL>Z0

)/(1

1

0LL jXRjBjXZ ++

+=

For a match looking into the matching network, we have

Solving for X and B from the two equations for real and

imaginary parts,

22

0

22

0/

LL

LLLLL

XR

RZXRZRXB

+

+=

*Note:B is always real (RL

>Z0) and has two solutions. One solution

is capacitive (positive) and the other one is inductive (negative).


LL

L

BR

Z

R

ZX

BX 00

1+=

and

Both solutions are applicable for impedance matching at a

single frequency. But one solution may be preferable over

the other one when other performance, e.g. frequencyresponse, is considered.

Case 2: load impedance outside the 1+jx circle --->RL

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Example:

1

Figure 1: Transmitter to antenna matching circuit design.


Solution:

Step 1: Compute normalized transmitter and antenna

impedances. Since no characteristic impedanceZ0 is given,

we arbitrarily selectZ0 = 75 for simplicity.

We have zT=ZT/Z0 = 2 +j 1

zA =ZA/Z0 = 1 +j 0.2

Step 2: Taking into account the first element (the shunt

capacitor) connected to the transmitter.

Move down on the circle of the constant conductance.

Step 3: Taking into account the next element (the series

inductor) connected to the transmitter.

Move up on the circle of the constant resistance.


Step 4: Draws the complex conjugate of the antenna

impedance in the Smith Chart for maximum power

transfer. This should be the output impedance of the

matching network.

zM=zA* = 1 -j 0.2

Step 5: Find the normalized impedance of the intersection

of two circles.zTC= 1 -j 1.22 and the corresponding

admittance ofyTC= 0.4 +j 0.49.

The normalized susceptance of the shunt capacitor is

jbC=yTC- yT=j 0.69

and the normalized reactance of the inductor is

jxL =zA - zTC=j 1.02 nHZxL L 09.6/)( 0 ==

pFZbCC

73.0)/(0

==


Design of the

matching network

using ZY Smith

Chart

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There is another path connectingzMandzY.

What does this mean?

1 Find the normalized source and load impedances.

2 In the Smith Chart, plot circles of constant resistance andconductance that pass through the point denoting the source

impedance.

3 Plot circles of constant resistance and conductance that pass

through the point of the complex conjugate of the load

impedance.

4 Identify the intersection points between the circles in steps 2 and

3. The number of intersection points determines the number ofpossible L-section matching networks. (cont)

Procedures of designing impedance matching networks using

Smith Chart


5 Find the values of the normalized reactances and susptances

of the inductors and capacitors by tracing a path along the

circles from the source impedance to the intersection point

and then to the conjugate of the load impedance.

--- there are usually multiple paths (multiple solutions).

6 Determine the actual values of inductors and capacitors for a

given frequency.

Design procedures cont

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