Microwave Electronics: Impedance Matching Techniques

ELEC 401 – Microwave Electronics ELEC 401 MICROWAVE ELECTRONICS Lecture on Matching Instructor: M. İrşadi Aksun Acknowledgements: M. I. Aksun Koç University 1/28 ELEC 401 – Microwave Electronics Outline  Chapter 1: Motivation & Introduction  Chapter 2: Review of EM Wave Theory  Chapter 3: Plane Electromagnetic Waves  Chapter 4: Transmission Lines & Smith Chart  Chapter 5: Microwave Network Characterization Chapter 6: Impedance Matching  Chapter 7: Passive Microwave Components M. I. Aksun Koç University 2/28 ELEC 401 – Microwave Electronics Impedance Matching Impedance matching or tuning is important, because it helps to  transfer maximum power to the network or load;  improve the signal-to-noise ratio of the system Z0 Matching Network Load  Matching networks are ideally lossless, and  it is always possible to design such a matching network if the load has some non-zero real part M. I. Aksun Koç University 3/28 ELEC 401 – Microwave Electronics Impedance Matching I. Matching with lumped elements (L Networks):  L section uses two reactive elements to match an arbitrary load impedance to a TL;  There are two possible configurations; jX jX Z0 jB ZL Z L is inside the 1+jX circle on the SC M. I. Aksun Koç University Z0 jB ZL Z L is outside the 1+jX circle on the SC 4/28 ELEC 401 – Microwave Electronics Impedance Matching jX Z0 jB ZL Z L is outside the 1+jX circle on the SC jX 1  jX Z0 jB ZL Z L is inside the 1+jX circle on the SC M. I. Aksun Koç University 5/28 ELEC 401 – Microwave Electronics Impedance Matching Comments on the use of lumped elements:  Actual lumped element capacitors and inductors can be used up to several GHz. However,  there is a large range of frequencies and circuit sizes where lumped elements cannot be realized. This is considered to be the major limitation of the L-Section matching network. M. I. Aksun Koç University 6/28 ELEC 401 – Microwave Electronics Impedance Matching Frequency response of a real lumped inductor: M. I. Aksun Koç University 7/28 ELEC 401 – Microwave Electronics Impedance Matching Frequency response of a real lumped capacitor: M. I. Aksun Koç University 8/28 ELEC 401 – Microwave Electronics Impedance Matching Realization of inductors and capacitors from TL sections  A small section of high impedance line is equivalent to a series inductance: Z 01 Z0 Z 02 Z L  Z 02 Z  jZ0 tan l Z  jZ0l Z 0  Z L Z in  Z 0 L  Z0 L    Z L  jZ0l Z 0  jZ L tan l Z 0  jZ Ll Z l Z in  Z L  j 0  Z L  jL v M. I. Aksun Koç University 9/28 ELEC 401 – Microwave Electronics Impedance Matching Realization of inductors and capacitors from TL sections  A small section of low impedance line is equivalent to a shunt capacitance: Z 01 Z0 Z 02 YL  Y02 Y  jY0 tan l Y  jY0l Y0 YL Yin  Y0 L  Y0 L   YL  jY0l Y0  jYL tan l Y0  jYLl Yl Yin  YL  j 0  YL  jC v M. I. Aksun Koç University 10/28 ELEC 401 – Microwave Electronics Impedance Matching Example: Design an L section matching network to match a load ZL=(100-j50)W to a 50 W line at 1.0 GHz. Z L  2  j1 is inside the 1+jX circle jX Z0 jB ZL Y1  YL  jB YL  0.4  j 0.2 M. I. Aksun Koç University ZL 11/28 ELEC 401 – Microwave Electronics Impedance Matching 1. Z L  2  j1  YL  0.4  j 0.2 21. Y1  YL  j 0.3  Z1  1  j1.2 3. Z in  Z1  j1.2  1.0 j 0.3 4. B  0.3; X  1.2 YL jX Z0 Z2 Y1 jB ZL ZL Y1  YL  jB YL  0.4  j 0.2 Y2 Z1 22. Y2  YL  j 0.7  Z 2  1  j1.2 3. Z in  Z 2  j1.2  1.0 4. B  0.7; X  1.2 M. I. Aksun Koç University 12/28 ELEC 401 – Microwave Electronics Impedance Matching B 6 10 3 3 Capacitive 3 B  0.3  B   6 10 / W  B  C  C   pF 50 2 1109  60 30 Inductive  nH X  1.2  X  X  50  60W  X  L  L  9  2 110 jX Z0 jB ZL Y1  YL  jB YL  0.4  j 0.2 B 1 50 L H 9 L 0.7  2 110 X  1.2  X  X  50  60W  X  1 1 C  F 9 C 60  2 110 0.7 Inductive B  0.7  B  / W    50 Capacitive M. I. Aksun Koç University 13/28 ELEC 401 – Microwave Electronics Impedance Matching II. Single Stub matching Yin Ys Y0 Y0 ZL Y Y0 Open Circuit or Short Circuit d l In single stub tuning, the two adjustable parameters are the distance d from the load to the stub position, and the length of the stub l. M. I. Aksun Koç University 14/28 ELEC 401 – Microwave Electronics Impedance Matching  The basic idea is to select d so that Y  Y0  jB, and  jB jB  to find the length of the stub l such that Ys   jB, hence Yin  Y 0  Y Yin M. I. Aksun Koç University Y0 ZL Y Y0 Open Circuit or Short Circuit d Ys Y0 Ys l 15/28 ELEC 401 – Microwave Electronics Impedance Matching  Example: Design two single-stub shunt tuning networks to match Z L  (15  j10)W to a 50W line. Solution: - There are two approaches to solve such a problem; using Smith Chart and using analytical expressions of TL. - Solution with Smith Chart is more intuitive, and easier than solving the problem analytically. Yin Ys Y0 M. I. Aksun Koç University Y0 ZL Y Y0 Open Circuit or Short Circuit d l 16/28 ELEC 401 – Microwave Electronics Impedance Matching Solution via Smith Chart: Z (15  j10) i) Z L  L   0.3  j 0.2 Z0 50 ii) Draw the corresponding SWR circle or constant G circle. iii) YL  2.2  j1.5 Note that the SWR circle intersects the 1+jb circle at two points. Y2 ZL YL d1  0.042 d2  0.385 Yin Ys Y0 Y0 ZL Y1 Y Y0 Open Circuit or Short Circuit d l M. I. Aksun Koç University 17/28 ELEC 401 – Microwave Electronics Impedance Matching iv) Y1  1.0  j1.33 Y2  1.0  j1.33 Ys  j1.33 v) The first tuning solution requires a stub with Ys  j1.33 vi) The length of an opencircuited stub that gives this susceptance can be found on the SC by starting at Y  0 (open  circuit ) l1  0.147 l2  0.353 Yin d Ys Y0 Y Y0 Open Circuit Y 0 Y0 ZL Ys   j1.33 l M. I. Aksun Koç University 18/28 ELEC 401 – Microwave Electronics Impedance Matching  0 Z Open Circuit Zin  (75  j90)W Z L  60  j 45W Ys 75 W Zin  (75  j90)W Z 0  75W Z 0  75W Z 0  75W d Z L  60  j 45W  Example: For a load impedance of ZL=(60-j45)Ω, design two single-stub matching networks that transform the load to a Zin=(75+j90)Ω input impedance. Assume that both stub and transmission line shown below have a chracteristic impedance of Z0=75Ω. l Microstrip realization M. I. Aksun Koç University 19/28 ELEC 401 – Microwave Electronics d j 0.45  Ys1 Zin  (75  j90)W Z 0  75W Z in  W 75 Z 0 YL Ys Open Circuit l  j1.6  Ys 2 ZL Yin ZL  60  j 45  0.8  j 0.6 75 75  j 90  1.0  j1.2 75 YL  0.8  j 0.6 Z in  Ys1  j 0.45 M. I. Aksun Koç University Ys 2   j1.6 20/28 Z L  60  j 45W Impedance Matching ELEC 401 – Microwave Electronics Impedance Matching d YL  Ys1 Zin  (75  j90)W Z 0  75W YL Open Circuit Yin Y L  Ys 2 Z0  Ys W 75 l YL  Ys1  Yin YL  Ys 2  Yin M. I. Aksun Koç University d2=(0.416-0.35)=0.066 21/28 Z L  60  j 45W  Find the length d of the TL; ELEC 401 – Microwave Electronics Impedance Matching d Zin  (75  j90)W l1=0.067 Z 0  75W Open Circuit Y 0 Z0  Ys W 75 Z L  60  j 45W  Find the length l of the stub; Ys1  j 0.45 l Starting from the opencircuit Y  0, one can move towards generator to reach Ys1  j 0.45 Ys1   j1.6 M. I. Aksun Koç University Ys 2   j1.6 22/28 ELEC 401 – Microwave Electronics Impedance Matching II. Double-Stub matching YB YA Yin YC d Y0 jB2 Y0 O.C or S.C. l2 jB1 Y0 Y0 O.C or S.C. Y0 YL Y l1  In double-stub tuning, the two adjustable parameters are the lengths of the stubs, l1 and l2.  Note that the distance between the two stubs d is usually set to a fixed value /8 or 3/8. M. I. Aksun Koç University 23/28 ELEC 401 – Microwave Electronics Impedance Matching  The operation of this tuner: i. For a perfect match Yin  1  YC  1  jB2 . YC point must be located on the G  1 circle. YB YA Yin YC d G  1 Circle Y0 jB2 Y0 Yin  1 M. I. Aksun Koç University O.C or S.C. l2 jB1 Y0 Y0 O.C or S.C. Y0 YL Y l1 24/28 ELEC 401 – Microwave Electronics Impedance Matching  The operation of this tuner: ii. YB point must lie on the rotated G  1 circle YB YA Yin YC d Y0 jB2 Y0 Yin  1 Forbidden Region O.C or S.C. G  1 circle l2 jB1 Y0 Y0 O.C or S.C. YL Y0 Y l1 is rotated towards load by the distance d. YB  YA  jB1. M. I. Aksun Koç University 25/28 ELEC 401 – Microwave Electronics • Design of a double-stub matching network It is assumed that in the double-stub matching network seen below, the lengths of the TLs are l1=λ/8 and l3=l2=3λ/8. Find the lengths of the short circuited stubs that match the load impedance ZL=(50+j50)Ω to a 50Ω input impedance. The chracteristic line impedance for all components is Z0=50Ω M. I. Aksun Koç University 26/28 ELEC 401 – Microwave Electronics Z L  1  j1W YD  0.4  j 0.2S 0.125 Z D  2  j1W M. I. Aksun Koç University 27/28 ELEC 401 – Microwave Electronics 3 / 8 towards load MAKE SURE THAT YD IS NOT INSIDE THE FORBIDDEN REGION YB  1 j3S The difference between YD and YC is: YD  YC   j 2 S  jBS1   j 2S YD  0.4  j 0.2S  jX S1  j 0.5W YA  1S Forbidden Region Therefore the length of first stub is lS1 = 0.074λ. The difference between YB and YA is: 3 / 8 towards generator YC  0.4  j1.8S YB  YA   j3S  jBS1   j 3S  jX S1  j 0.33W M. I. Aksun Koç University Therefore the length of second stub is lS2 =28/28 0.051λ.

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