1. Chap5. Impedance Matching circuits
강원대학교
전기전자공학부

2. Introduction to impedance matching
In electronics, impedance matching is the designing practice to maximize the power transfer or minimize signal reflection from the load.
In the case of a complex source impedance ZS and load impedance ZL, maximum power transfer is obtained when they are in complex conjugate relation.
In the case of the figure below, the impedance matching is obtained when
Though the concept of impedance matching found first applications in electrical engineering, that is useful in other energy transfer applications such as mechanical power transfer with a gear system.
Zin

3. *High impedance bridging
In electronics, especially DC power supply, audio frequency system, a high impedance bridging is another type of impedance matching concept in which the source impedance is much smaller than the load impedance for high fidelity.
In cases where the load impedance can not be fixed, minimizing the source impedance serves to both minimize the current drawn by the load and maximize the voltage signal across load, and vise versa.
In audio amplifier, the input impedance of modern op-amp circuits is often naturally much higher than the signal source. The value of the output impedance is also usually desired to be significantly lower than the load impedance. When driving loudspeakers the damping factor, DF is:
The concept of the high impedance bridging

4. *Impedance matching examples
In microwave circuits and systems including antenna, each block is matched at Z0 of the corresponding transmissions lines.
Telephone systems use matched impedances to minimize echo(Г=0) on long-distance lines using the telephone hybrid coil.
On the power grid the overall load is usually inductive. Consequently, power factor correction is most commonly achieved with banks of capacitors. This causes the load seen by the power line to be purely resistive.
In medical ultrasonography, without the gel, the impedance mismatch in the transducer-to-air and the air-to-body discontinuity reflects almost all the energy, leaving very little to go into the body.
The bones in the middle ear provide impedance matching between the eardrum and the fluid-filled inner ear.
When light goes through the interface between two media with different refractive indices, Unwanted reflections can be reduced by the use of an anti-reflection optical coating.

5. Introduction
Matching network is ideally a lossless network which matches an arbitrary load impedance with non-zero real part to the Z0 of the T.L.
Matching is important for the following reasons;
Maximum power transfers when the load is matched to the generator.
Matching sensitive Rx components(such as ANT, LNA, etc) improves S/N ratio or sensitivity of the system.
Impedance matching in a power distribution network (such as an ANT array feed network) will reduce amplitude and phase errors.
Impedance matching reduces the reflection wave in the transmission lines and unwanted spurious and harmonic signal by the nonlinear devices in the system. Z0

6. Matching Network Selection Criteria
Complexity : A simpler impedance transformation network is usually cheaper, more reliable, and less lossy than a more complex design.
Bandwidth : Typical matching network gives only match at single frequency. For wide band matching, the circuit complexity will be increased (for instance multi-section transformers).
Implementation : Short-circuited stubs are easy to implement in coax and waveguide. Open-circuited stubs are much easier in stripline and microstrip lines.
Adjustability : Some applications may require adjustments or tuning.

7. 5.1 Matching with lumped elements (L-networks)
Simplest type matching is the L-section with 2 reactive elements (capacitor and inductor)
Choose (a), if zL=ZL/Z0 is inside the 1+jx circle : red
Choose (b), if zL=ZL/Z0 is outside the 1+jx circle : white
Limitation of use
Small lumped element should be used
Frequency range : below some GHz
1+jx circle
or unit r circle

8. Analytic Solutions Case (a) : zL=ZL/Z0 is inside the 1+jx circle
Zin = Z0 for matching
Two solution 중 소자값, matching BW등을 고려해서 선택한다.

9. Cont’ Case (b) : zL=ZL/Z0 is outside the 1+jx circle
1/Zin = 1/Z0 for matching
Two solution 중 소자값, matching BW등을 고려해서 선택한다.

10. Smith Chart Solutions L C

11. Cont’
* Impedance chart 와 admittance chart가 동시에 있는 smith chart를 사용하면 z 와 y간의 converting 없이 가능. C L
jb=j0.3
jx=1.2
zL=2-j

12. Cont’
동일한 문제의 또 다른 solution C L
jb=j0.69
jx=1.22
zL=2-j

13. Cont’
두 solution의 비교

14. Lumped Elements for Microwave Circuits
Lumped R,L,C elements can be practically realized at microwave frequencies, if the length (l) condition l < λ/10 is satisfied.
SMD Chip RLC : 0.5pF~수십 pF, 수 nH~수십nH. 0Ω~수백 Ω
Range : 0402~2220
ex: 0603=0.6mm×0.3mm

15. 5.2 Single-Stub Tuning
A single open circuited or short circuited transmission line (a stub), connected either in parallel or in series with the transmission line at a certain distance(d) from the load.
The shunt tuning stub is especially easy to fabricate in microstrip or stripline form.
Two adjustable parameters
(1) distance(d) from load to stub
(2) value of susceptance or reactance by stub
Figure 5.4 Single-stub tuning circuits. (a) Shunt stub. (b) Series stub.

16. Example 5.2
Question: ZL=60-j80Ω (zL=1.2-j1.6), design two single shunt stub tuning networks for a 50 Ω line, at 2GHz.
0.155λ ( =0.405)
0.176λ
Sol: Admittance Smith Chart 사용
(1) zL, yL 포함하는 constant-SWR circle
(2) 1+jb circle과의 두 교점 : y1, y2
(3) d1= =0.110λ
d2= =0.260λ
(4) y1=1+j1.47, y2=1-j1.47
(5) for 1.00+j0.00 : -j1.47, j1.47필요
l1=0.095λ, l2=0.405λ
0.065λ d1 y1 yL
1+jb circle
short d2
constant SWR circle zL l1 l2 d1 d2 l2 y2 l1
0.345λ
( =0.095)
0.325λ

17. Comparison of two solutions

18. Example 5.3
Question: ZL=100+j80Ω, design two single series stub tuning networks for a 50 Ω line, at 2GHz.
0.147λ
( =0.397)
Sol: impedance Smith Chart 사용
(1) plot zL=2.0+j1.6, and constant SWR circle
(2) two intersections with 1+jx curve : x1, x2
(3) d1= =0.120λ
d2=( )+0.172=0.463λ
(4) z1=1-j1.33, z2=1+j1.33
(5) for 1.00+j0.00 :+j1.33, -j1.33 필요
l1=0.397λ, l2=0.103λ zL z2 d2
1+jx circle
open d1
constant SWR circle z1
0.353λ
( =0.103)

19. Example 5.3
Comparison of two solutions

20. 5.3 Quarter wave transformer
A useful circuit for matching a real load to a transmission line
Increased BW for smaller load mismatches
A single-section quarter-wave matching transformer.
at the design frequency

21. 5.4 Multisection transformer
The matching bandwidth can be increased by using a multisection transformer
Binomial multisection matching transformer
Chebyshev multisection matching transformer
N equal-length(λ/4) sections
of transmission lines
Binomial multisection
Chebyshev multisection

22. 5.5 Tapered lines
If the N of the Multisection transformer increase, the transformer geometry approaches a continuously tapered line.
Exponential taper
Triangular taper
Klopfenstein taper

23. 5.6 More advanced matching
A better matching network may have the required bandwidth and the ability of matching to an arbitrary impedance.
More advanced matching network design is possible with various filters;
Lowpass filters
Highpass filters
Bandpass filters