116/11/50 ENE 490 Applied Communication Systems Lecture 2 circuit matching on Smith chart

216/11/50 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 Z 0 is a characteristic impedance of a transmission line. Assume the line is lossless.

316/11/50 Review (2)  Terminated lossless line –voltage reflection coefficient – impedance along a transmission line or

416/11/50 Review (3) - voltage standing wave ratio  source and loaded transmission line

516/11/50 Review (4)  power transmission of a transmission line  for lossless and a matched condition  power in decibels

616/11/50 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.

716/11/50 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.

816/11/50 Ex1 Adding a series inductor L (z L = j0.8) to an impedance z = 0.3-j0.3.

916/11/50 Ex2 Adding a series capacitor C (z C = - j0.8) to an impedance z = 0.3-j0.3.

1016/11/50 Ex3 Adding a shunt inductor L (y L = - j2.4) to an admittance y = 1.6+j1.6.

1116/11/50 Ex4 Adding a shunt capacitor C (y C = j3.4) to an admittance y = 1.6+j1.6.

1216/11/50 Examples of matching network design Ex5 Design a matching network to transform the load Z load = 100+j100  to an input impedance of Z in = 50+j20 .

1316/11/50 Ex6 Design the matching network that provides Y L = (4-j4)x10 -3 S to the transistor. Find the element values at 700 MHz.

1416/11/50 L matching networks

1516/11/50 Forbidden regions Sometimes a specific matching network cannot be used to accomplish a given match.

1616/11/50 Load quality factor  The developed matching networks can also be viewed as resonance circuits with f 0 being a resonance frequency. These networks may be described by a loaded quality factor, Q L.  The estimation of Q L is simply accomplished through the use of a so-called nodal quality factor Q n. At each node of the L-matching networks, there is an equivalent series input impedance, denoted by R S +jX S. Hence a circuit node Q n can be defined at each node as

1716/11/50 Circuit node Q n and loaded Q L L-matching network is not a good choice for a design of high Q L circuit since it is fixed by Q n. 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 Q n.

1816/11/50 The example of Q calculation At 500 MHzQ n = 2 then Q L = 1. and = 500 MHz

1916/11/50 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.

2016/11/50 Constant Q n contours

2116/11/50 The upper and lower part of Q contours satisfy a circle equation. Since then which can be written as

2216/11/50 Contour equations The equations for these contours can be derived from the general derivation of the Smith chart. By following the derivation, Q n contours follow this circle equation, where the plus sign is taken for positive reactance x and the minus sign for negative x.

2316/11/50 Q n circle parameters For x > 0, the center in the  plane is at (0, -1/Q n ). For x < 0, the center in the  plane is at (0, +1/Q n ). the radius of the circle can be written as

2416/11/50 Ex8 Design two T networks to transform the load impedance Z L = 50  to the input impedance Z in = 10-j15  with a Q n of 5.

2516/11/50 Ex9 Design a Pi network to transform the load impedance Z load = 50  to the input impedance Z in = 150  with a Q n of 5.