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Impedanc matching
- 2. L o a d i n g 2
- 3. Microwave Device & Integrated Circuit Technology The Republic of Iraq University of technology Electrical department 3
- 4. 4
- 5. 1 2 3 4 5 6 7 Introductio n Review of smith chart Impedance matching Conversing between series and parallel RL & Tapped capacitor and inductor The concept of mutual inductance Matching using transformer 8 9 1 0 1 1 1Tuning a transformer The bandwidth of un impedance transformation network Quality factor of an LC resonant Transmission l S. Y. and Z parameters5
- 6. 1 2 3 Resistance 𝛺 Reactance 𝛺 Impedance 𝛺 W h a t i s t h e d i f f e r e n c e 1-Introduction 6
- 7. In RF there is parasitic behavior appear in high frequency Example Low frequency High frequency 7
- 8. 50𝛺 50𝛺 50𝛺 Rl 50𝛺would like 50𝛺 here Transmission line Rs Vin Circuit Transmission line 25𝛺 50𝛺 a very popular impedance WHY 8
- 9. 𝑧𝑖𝑛 = 50 − 𝑗30 50 𝛺50 𝛺 +𝑗30 why we use matching Some matching circuit must always be added circuit to be match 9
- 10. 2-Review of smith chart Go to program 10
- 11. 3-Impedance matching The input impedance of a circuit can be any value. In order to have the best power transfer into the circuit, it is necessary to match this impedance to the impedance of the source driving the circuit. By using reactive componentWHY They not absorb any power They not add any noise 11
- 12. *Series components will move the impedance along a constant resistance circle on the Smith chart. Parallel components will move the admittance along a constant conductance circle. *Using lumped component to match circuit* 12
- 14. There are eight possible two component matching networks, also known as ell networks 𝐿 𝑠 𝐿 𝑝𝐶 𝑝 𝐶𝑆 𝐿 𝑠 𝐶 𝑝 𝐿 𝑠 𝐿 𝑠 𝐿 𝑝 𝐶𝑆 𝐶𝑆 𝐶𝑆 𝐶 𝑝𝐶 𝑝𝐿 𝑝𝐿 𝑝 14
- 15. 𝐿 𝑠 𝐿 𝑝 𝐶𝑆 𝐶 𝑝𝐿 𝑝𝐿 𝑠 𝐶 𝑝𝐶𝑆 𝒛 = 𝟎 𝒀 = ∞ 𝒛 = ∞ 𝒀 = 𝟎 𝒀 = 𝟏 − 𝒋𝑩 𝒀 = 𝟏 + 𝒋𝑩 Z = 𝟏 − 𝒋𝑿 Z = 𝟏 + 𝒋𝑿 15
- 16. EX: A possible impedance-matching network is shown in Figure Use the matching network to match the transistor input impedance Zin = 40 - j30 Ω to Zo = 50Ω. Perform the matching at 2GHz. C2 𝑧𝑖𝑛 𝑌𝑖𝑛𝐨𝐫 𝑧2 𝑌2𝐨𝐫 𝑧3 𝑌3 = 𝑌0 𝑧0 = 16
- 17. solve 𝜔𝐿 = 𝑋𝑖𝑛 + 𝑅 𝑖𝑛−𝑦0 𝑅𝑖𝑛 2 𝑌0 30 + 40−(0.02)(40)2 0.02 = 50 2𝜋𝑓𝐿 = 50 𝐿 = 3.97 𝑛𝐻 𝜔𝐶 = 𝜔𝐿 − 𝑋𝑖𝑛 𝑅𝑖𝑛 2 + (𝜔𝐿 − 𝑥𝑖𝑛)2 50 − 30 402 + (50 − 30)2 = 0.01 1 2𝜋𝑓𝑐 = 0.01 𝐶 = 796 𝑓𝐹 17
- 18. Example :- General Matching Example Match Z = 150 - 50j to 50Ω using the techniques just developed Go to program 18
- 19. When we arbitrary adding parallel capacitor it will moving the point A to point B and the series inductor will move the point B to point C 19
- 20. 4-conversion between series and parallel resistor – inductor and resistor – capacitor circuit 𝑅 𝑠 𝐶𝑠 𝐶 𝑝 𝑅 𝑝 𝐿 𝑠 𝑅 𝑠 𝐿 𝑝 𝑅 𝑝 Series and parallel resistor-capacitor (RC) and resistor-inductor (RL) networks are widely used basic building blocks of matching networks 20
- 21. How to fined the parameters 𝑧 = 𝑅 𝑠 + 1 𝑗𝑤𝐶𝑆 𝑌 = 𝑗𝜔𝐶 + 𝜔2 𝑐 𝑠 2 𝑅 1 + 𝜔𝐶𝑠 2 𝑅 𝑠 2 𝑅 𝑝 = 1 + 𝜔𝐶𝑠 2 𝑅 𝑠 2 𝜔2 𝑐 𝑠 2 𝑅 = 𝑅 𝑠(1 + 𝑄2) 𝐶 𝑝 = 𝐶𝑠 1 + 𝜔𝐶𝑠 2 𝑅 𝑠 2 = 𝐶𝑠 𝑄2 1 + 𝑄2 21
- 22. 5-Tapped capacitor an inductor In this case, the two inductors or two capacitors act to transform the resistance into a higher equivalent value in parallel with the equivalent series combination of the two reactance's. 22
- 23. 23
- 24. 6-the concept of mutual inductance Any two coupled inductors that affect each other’s magnetic fields and transfer energy back and forth form a transformer 𝒌 = 𝒎 𝑳 𝑷 𝑳 𝑺 Coupling factor L primary L secondary Mutual inductance 24
- 25. I1 I2 I3 25
- 26. 𝐿 𝑃 𝐿 𝑠 𝑀 𝐿 𝑃 − M 𝐿 𝑠 − M M An equivalent model for the transformer that uses mutual inductance is. This model can be shown to be valid if two of the ports are connected together as shown in the figure by writing the equations in terms. 26
- 27. Ex: Equivalent Impedance of Transformer Networks Referring to the diagram of Figure 4.20, find the equivalent impedance of each structure, noting the placement of the dots. 27
- 28. 7- matching using transformer Transformers, can transform one resistance into another resistance depending on the ratio of the inductance of the primary and the secondary. Assuming that the transformer is ideal (that is, the coupling coefficient k is equal to 1 28
- 29. 8-tuning a transformer Unlike the previous case where the transformer was assumed to be ideal, in a real transformer there are losses 29 Go to program
- 30. Ex: Mic Load speaker 10000 Ω 100 Ω N1 N2 For maximum power transfer 𝐾 = 𝑍 𝐿 𝑍𝑠 = 10000 100 = 10 𝑘 = 𝑁2 𝑁1 30
- 31. 31 9-The bandwidth of an impedance transformation network It can defined the bandwidth as the difference between two frequencies Denoted by( F lower) and (F upper ) In other word it’s the range when the circuit work in best performance with less Power dispersion
- 32. 32 3dB Bandwidth Center frequency f A *Most equivalent matching circuit are either RLC parallel or RLC series
- 33. 33 10-quality factor of an LC resonator The Q (quality factor) of an LC resonator is another figure of merit used. It is defined as 𝑄 = 2𝜋 𝐸𝑠𝑡𝑜𝑟𝑒𝑑 𝐸𝑙𝑜𝑠𝑠 Or another way to find Q is 𝑄 = 𝜔𝑜 2 𝑑𝜙 𝑑𝜔 Rate of change of the phase transfer function
- 34. 34 The relation ship between the quality factor and the frequency with the bandwidth is defined as 𝑄 = 𝜔0 𝐵𝑊
- 35. 35 A circuit has an input that is made up of a 1-pF capacitor in parallel with a 200-Ω resistor. Use a transformer with a coupling factor of 0.8 to match it to a source resistance of 50Ω. The matching circuit must have a bandwidth of 200 MHz and the circuit is to operate at 2 GHz. 𝐶𝑡𝑜𝑡𝑎𝑙 = 1 𝑅𝐵𝑊 = 1 100 ∗ (2 𝜋 ∗ 200𝑀𝐻𝑧) = 7.96𝑝𝐹 𝐿 𝑠 = 1 𝜔0 2 𝐶𝑠 = 1 (2 𝜋 ∗ 2𝐺𝐻𝑧)2∗ 7.96 𝑝𝐹 = 0.8𝑛𝐻 𝐿 𝑝 = 𝑅 𝑒𝑓𝑓 𝑅 𝐿 𝐿 𝑠 𝑘2 𝑅 𝐿 2 − 𝑊0 2 𝐿 𝑠 2 (1 − 𝑘2)2 = 50𝛺 ∗ 200𝛺 ∗ 0.8𝑛𝐻 ∗ (0.8)2 (200𝛺)2−(2𝜋 ∗ 2𝐺𝐻𝑍)2(0.8𝑛𝐻)2(1 − 0.82)2 = 0.13𝑛𝐻
- 36. 11-transmission line When designing circuits on chip, transmission line effects can often be ignored, but at chip boundaries they are very important 36
- 37. 12- s y and z parameter Scattering parameter Admittance parameter Impedance parameter 37
- 38. Why the S parameter is important in communication ????????????????? S-parameters do not use open or short circuit conditions to characterize a linear electrical network instead, matched loads are used. These terminations are much easier to use at high signal frequencies than open-circuit and short-circuit terminations. 38
- 39. ZLZo Zo a b if Zo = ZL then b=0 and that’s mean ( perfect ) b = S a Reflected Incoming ……………………………………………………...For one port. 39
- 40. 40 𝑏1 𝑏2 𝑏3 = 𝑆11 𝑆12 𝑆13 𝑆21 𝑆22 𝑆23 𝑆31 𝑆32 𝑆33 𝑎1 𝑎2 𝑎3 For more 0ne port use matrix 𝑏1 = 𝑆11 𝑎1 + 𝑆12 𝑎2 + 𝑆13 𝑎3
- 41. a1 b1 a2 b2 a3 b3 = 𝑏1 𝑎1 𝑎2 = 𝑎3 = 0S11 S21 = 𝑏2 𝑎1 𝑎2 = 𝑎3 = 0
- 42. 42 𝑉1 = 𝑍11 𝐼1 + 𝑍12 𝐼2 𝑉2 = 𝑍11 𝐼1 + 𝑍12 𝐼2 Z-Parameter
- 43. 43 I1 V1 Z11 = 𝑉1 𝐼1 𝐼2 = 0 Z21 = 𝑉2 𝐼1 𝐼2 = 0
- 44. 44