Chapter 5. Impedance matching and tuning

Maximum power delivered when applied to matched load Zs = 20  + V - Z0= 50  ZL= 1k 

Ringing ~ Signal source Load Mismatched load

Impedance matching - Digital Source matching ~ Load matching ~

Impedance matching – RF회로 Maximum power transfer ~ Source matching Load matching

Matching with lumped elements Figure 5.2 (p. 223) L-section matching networks. (a) Network for zL inside the 1 + jx circle. (b) Network for zL outside the 1 + jx circle.

Analytic solution

Example 5.1 Smith chart – impedance chart ZL= 200-j 100  Z0= 100  Figure 5.3a (p. 226) Solution to Example 5.1. (a) Smith chart for the L-section matching networks. ZL= 200-j 100  3 Z0= 100  f = 500MHz 2 5 1 4 Smith chart – impedance chart

Impedance-admittance chart ZL= 200-j 100  Z0= 100  f = 500MHz 0.0 1 0.2 Add series L Add shunt C 0.5 1.2

Basic Smith chart operation 1. Translation 2. Add series element L C

3. Add shunt element L C

Constant resistance, reactance circles x r=0 r=0.5 r=1 r=2 R 0.5 1 2 x 2 x=1 x=0.5 1 x=2 0.5 R 0.5 1 x=-2 x=-1 x=-0.5 2

5.2 Single stub tuning ZL= 60-j 80  Z0= 50  f = 2GHz Translate by ‘d’ 1 1 0.314 0.314 0.422 D를 변화시켜 1+jb 원의 원주 상에 yL이 오도록 한다.

Add shunt stub (shorted) 1+jb 원의 원주 상의 지점을 shunt stub(병렬 stub)을 달아서 Γ원의 원점으로 옮기면 impedance matching이 완료됨.

0.422 0.314 Impedance matching 순서 zL이 1+jb 원의 원주 상에 올 수 있도록 d1을 조절한다. (점선 원) 상에zL이 옮겨 올 수 있도록 L1을 조절한다. 1 0.314

Figure 5. 5b (p. 231) (b) The two shunt-stub tuning solutions Figure 5.5b (p. 231) (b) The two shunt-stub tuning solutions. (c) Reflection coefficient magnitudes versus frequency for the tuning circuits of (b).

5.3 Double stub tuning Figure 5.7 (p. 236) Double-stub tuning. (a) Original circuit with the load an arbitrary distance from the first stub. (b) Equivalent-circuit with load at the first stub. Single stub의 경우 d와 L을 둘 다 변화시켜야 하는 불편한 점이 있었으나, double stub인 경우 d는 고정되는 장점이 있다.

Impedance matching 순서 d가 고정되어 있으므로 1+jb 원을 반시계 방향으로 2βd (rad) 만큼 돌린다(점선 원). (점선 원) 상에zL이 옮겨 올 수 있도록 L1을 조절한다. (실선 원) 상에 있는 임피던스가 원점으로 옮겨 올 수 있도록 L2를 조절한다. 1

1

Single stub used in microwave circuits mixer Frequency doubler

5.4 Quarter-wave transformer Single section transformer at the design frequency f0. Figure 5.10 (p. 241) A single-section quarter-wave matching transformer.

5.5 Theory of small reflections

Multi-section transformer (Zn은 단조 증가 또는 감소.) (Γn이 대칭적인 경우)

5.6 Binomial multi-section matching transformer Example

Example 5.6 Design a three-section binomial transformer to match a 50Ω load to a 100 Ω line.

Figure 5.15 (p. 250) Reflection coefficient magnitude versus frequency for multisection binomial matching transformers of Example 5.6 ZL = 50Ω and Z0 = 100Ω. Гm=5% bandwidth 70%

Figure 5.16 (p. 251) The first four Chebyshev polynomials Tn(x). 5.7 Chebyshev multi-section matching transformer Figure 5.16 (p. 251) The first four Chebyshev polynomials Tn(x).

Design of Chebyshev transformers Determine A Determine BW

5.8 Tapered lines

Exponential taper