Analytic Solution for Shunt Stub

Problem 1: Repeat example 5.5 using analytic solution.

Example5.6: Design two single-stub (open circuit) series tuning networks to match this load ZL = 100+j 80 to a 50 line, at a frequency of 2 GHz? Solution 1. The normalized load impedance ZL= 2-j1.6. 2. SWR circle intersects the 1+jx circle at both points z1 = 1.0-j1.33 z2 = 1.0+j1.33. Reading WTG can obtain: d1= 0.328-0.208=0.12 d2= 0.672-0.208=0.463. 3. The stub length for tuning z1 to 1 requires l1 = 0.397, and for tuning z1 to 1 needs l2 = 0.103.

1. ZL = 100+j 80 at 2 GHz can find R= 100,L=6.37nH.

Analytic Solution for Series Stub

Problem 2: Repeat example 5.6 using analytic solution.

Shunt stubs are easier to implement in practice than series stubs. Double-Stub Matching adjustable tuning Variable length of length d between load and stub to have adjustable tuning between load and the first stub. Shunt stubs are easier to implement in practice than series stubs. In practice, stub spacing is chosen as /8 or 3/8 and far away 0 or /2 to reduce frequency sensitive. Original circuit Equivalent circuit

Disadvantage is the double-stub tuner cannot match all load impedances Disadvantage is the double-stub tuner cannot match all load impedances. The shaded region forms a forbidden range of load admittances. Two possible solutions b1,b2 and b1’,b2’ with the same distance d.

Example5.7: Design a double-stub (open circuit) shunt tuning networks to match this load ZL = 60-j 80 to a 50 line, at a frequency of 2 GHz? Solution 1. The normalized load impedance YL= 0.3+j0.4 (ZL= 1.2-j1.6). 2. Rotating /8 toward the load (WTL) to construct 1+jb circle can find two values of first stub b1 = 1.314 b’1 = -0.114. 3. Rotating /8 toward the generator (WTG) can obtain y2= 1-j3.38 y’2= 1+j1.38.

4. The susceptance of the second stubs should be 5. The lengyh of the open-circuited stubs are found as l1 = 0.146, l2 = 0.204, or l1 = 0.482, l2 = 0.350. 6.ZL = 60-j 80 at 2 GHz can find R= 60, C=0.995pF.

Analytic Solution for Double Stub

Problem 3: Repeat example 5.7 using analytic solution.

Quarter-Wave transformer It can only match a real load impedance. The length l= /4 at design frequency f0. The important characteristics

Example5.8: Design a quarter-wave matching transformer to match a 10 load to a 50 line? Determine the percent bandwidth for SWR1.5? Solution 

Binomial Multi-section Matching The passband response of a binomial matching transformer is optimum to have as flat as possible near the design frequency, and is known as maximally flat. The important characteristics

Binomial Transformer Design If ZL<Z0, the results should be reversed with Z1 starting at the end.

Example5.9: Design a three-section binomial transformer to match a 50 load to a 100 line? and calculate the bandwidth for m=0.05? Solution 

Using table design for N=3 and ZL/Z0=2(reverse) can find coefficient as 1.8337, 1.4142, and 1.0907.