ENE 490 Applied Communication Systems

1. ENE 490Applied Communication Systems Lecture 2 circuit matching on Smith chart

2. Review (1) • High frequency operation and its applications • Transmission line analysis (distributed elements) • Use Kirchholff’s law to obtain general equations for transmission lines • Voltage and current equations are the combination of incident and reflected waves. where Z0is a characteristic impedance of a transmission line. Assume the line is lossless.

3. Review (2) • Terminated lossless line • voltage reflection coefficient • impedance along a transmission line or

4. Review (3) - voltage standing wave ratio • source and loaded transmission line

5. Review (4) • power transmission of a transmission line • for lossless and a matched condition • power in decibels

6. Impedance matching network (1) • The need for matching network arises because amplifiers, in order to deliver maximum power to a load or to perform in a certain desired way, must be properly terminated at both the input and the output ports.

7. Impedance matching network (2) • Effect of adding a series reactance element to an impedance or a parallel susceptance are demonstrated in the following examples. • Adding a series reactance produces a motion along a constant-resistance circle in the ZY Smith chart. • Adding a shunt susceptance produces a motion along a constant-conductance circle in the ZY Smith chart.

8. Ex1 Adding a series inductor L (zL = j0.8) to an impedance z = 0.3-j0.3.

9. Ex2 Adding a series capacitor C (zC = -j0.8) to an impedance z = 0.3-j0.3.

10. Ex3 Adding a shunt inductor L (yL= -j2.4) to an admittance y = 1.6+j1.6.

11. Ex4 Adding a shunt capacitor C (yC= j3.4) to an admittance y = 1.6+j1.6.

12. Examples of matching network design • Ex5 Design a matching network to transform the load Zload = 100+j100  to an input impedance of Zin= 50+j20 .

13. Ex6 Design the matching network that provides YL = (4-j4)x10-3 S to the transistor. Find the element values at 700 MHz.

14. L matching networks

15. Forbidden regions • Sometimes a specific matching network cannot be used to accomplish a given match.

16. Load quality factor • The developed matching networks can also be viewed as resonance circuits with f0being a resonance frequency. These networks may be described by a loaded quality factor, QL. • The estimation of QLis simply accomplished through the use of a so-called nodal quality factor Qn. At each node of the L-matching networks, there is an equivalent series input impedance, denoted by RS +jXS. Hence a circuit node Qn can be defined at each node as

17. Circuit node Qn and loaded QL • L-matching network is not a good choice for a design of high QL circuit since it is fixed by Qn. • For more complicated configurations (T-network, Pi-network), the loaded quality factor of the match network is usually estimated as simply the maximum circuit node quality factor Qn.

18. The example of Q calculation • At 500 MHz Qn= 2 then QL = 1. and = 500 MHz

19. Ex7 The low pass L network shown below was designed to transform a 200 load to an input resistance of 200. Determine the loaded Q of the circuit at f = 500 MHz.

20. Constant Qncontours

21. The upper and lower part of Q contours satisfy a circle equation. • Since • then • which can be written as

22. Contour equations • The equations for these contours can be derived from the general derivation of the Smith chart. By following the derivation, Qncontours follow this circle equation, where the plus sign is taken for positive reactance x and the minus sign for negative x.

23. Qn circle parameters • For x > 0, the center in the  plane is at (0, -1/Qn). • For x < 0, the center in the  plane is at (0, +1/Qn). • the radius of the circle can be written as

24. Ex8 Design two T networks to transform the load impedance ZL= 50  to the input impedance Zin = 10-j15  with a Qnof 5.

25. Ex9 Design a Pi network to transform the load impedance Zload = 50 to the input impedance Zin= 150 with a Qnof 5.