1. Chapter 5.2 Chapter 5.3 SINGLE-STUB TUNING DOUBLE-STUB TUNING
Hogil Lee

2. Stub can be fabricated as part of the transmission line.
STUB TUNING
Matching technique uses a single open-circuited or short-circuited length of transmission line (a stub) connected either in parallel or in series with the transmission feed line at a certain distance from the load.
Advantage
Stub can be fabricated as part of the transmission line.
No lumped elements required.
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3. 5.2 SINGLE-STUB TUNING
Shunt stub
𝑌 𝐿 = 𝐺 𝐿 +𝑗 𝐵 𝐿 ↓
𝑌 0 +𝑗𝐵
𝑌 0
Series stub
𝑍 𝐿 = 𝑅 𝐿 +𝑗 𝑋 𝐿 ↓
𝑍 0 +𝑗𝑋
𝑍 0

4. 5.2 SINGLE-STUB TUNING
Transmission line media (microstrip, stripline) use open-circuited stubs since a via hole through the substrate to the ground plane is not needed.
Coax, waveguide use short-circuited stubs because the cross-sectional area may be large enough to radiate.

5. Shunt Stubs
𝒛 𝑳 = 𝒁 𝑳 𝒁 𝟎 =𝟏.𝟐−𝒋𝟏.𝟔
𝒚 𝑳 = 𝟏 𝒛 𝑳 =𝟎.𝟑+𝒋𝟎.𝟒

6. 𝑑=0.110𝜆 toward generator from 𝑦 𝐿
Shunt Stubs
𝑑=0.110𝜆 toward generator from 𝑦 𝐿
𝒚 𝑳 =𝟎.𝟑+𝒋𝟎.𝟒 ↓
𝒚 𝟏 =𝟏+𝒋𝟏.𝟒𝟕
𝒚 𝟏 →
𝒚 𝑳 →

7. 𝑙=0.095𝜆 toward generator from admittance short
Shunt Stubs
𝑙=0.095𝜆 toward generator from admittance short
𝒚 𝟏 =𝟏+𝒋𝟏.𝟒𝟕 ↓
𝒚 𝟎 =𝟏
+ 𝒚 𝒔 (−𝒋𝟏.𝟒𝟕)
𝒚 𝟏 →
𝒚 𝑳 →
↙ 𝒚 𝒔

8. Shunt Stubs
Solution #1(shorter length) has broader bandwidth.

9. Shunt Stubs
( 𝒀 𝟏 )
𝑌 𝐿 = 𝐺 𝐿 +𝑗 𝐵 𝐿 ↓
𝑌 0 +𝑗𝐵
𝑌 0
+ 𝒚 𝒔 (−𝒋𝟏.𝟒𝟕)
(𝑮= 𝒀 𝟎 )
𝑩 𝒔 =−𝑩
(5.11 a, b)
(𝑂𝑝𝑒𝑛 𝑠𝑡𝑢𝑏)
(𝑆ℎ𝑜𝑟𝑡𝑒𝑑 𝑠𝑡𝑢𝑏)

10. Series Stubs
𝒛 𝑳 = 𝒁 𝑳 𝒁 𝟎 =𝟐+𝒋𝟏.𝟔

11. 𝑑=0.120𝜆 toward generator from 𝑧 𝐿
Series Stubs
𝑑=0.120𝜆 toward generator from 𝑧 𝐿
𝒛 𝑳 =𝟐+𝒋𝟏.𝟔 ↓
𝒛 𝟏 =𝟏−𝒋𝟏.𝟑𝟑
𝒛 𝟏 →
𝒛 𝑳 →

12. 𝑙=0.397𝜆 toward generator from open
Series Stubs
𝑙=0.397𝜆 toward generator from open
𝒛 𝟏 =𝟏−𝒋𝟏.𝟑𝟑 ↓
𝒛 𝟎 =𝟏
+ 𝒛 𝒔 (+𝒋𝟏.𝟑𝟑)
𝒛 𝟏 →
𝒛 𝑳 →
↓ 𝒛 𝒔

13. Series Stubs

14. Series Stubs
( 𝒁 𝟏 )
𝑍 𝐿 = 𝑅 𝐿 +𝑗 𝑋 𝐿 ↓
𝑍 0 +𝑗𝑋
𝑍 0
+ 𝒛 𝒔 (+𝒋𝟏.𝟑𝟑)
(𝑹= 𝒁 𝟎 )
𝑿 𝒔 =−𝑿
(5.16 a, b)
(𝑆ℎ𝑜𝑟𝑡𝑒𝑑 𝑠𝑡𝑢𝑏)
(𝑂𝑝𝑒𝑛 𝑠𝑡𝑢𝑏)

15. 5.3 DOUBLE-STUB TUNING
Single-stub tuner requires a variable length of line between the load and the stub.
variable
The circuit can be designed in a fixed position by making it double-stub tuner.
However a double-stub tuner cannot match all load impedances.
fixed

16. Smith Chart Solution 𝑌 𝐿 = 𝐺 𝐿 +𝑗 𝐵 𝐿 ↓ 𝑌 1 = 𝐺 𝐿 +𝑗 𝐵 1 → 𝒃 𝟏 ( 𝒍 𝟏 )
𝒀 𝟐 →
𝒀 𝟏 →
𝑌 𝐿 = 𝐺 𝐿 +𝑗 𝐵 𝐿 ↓
𝑌 1 = 𝐺 𝐿 +𝑗 𝐵 1
𝑌 2 = 𝑌 0 +𝑗𝐵
𝑌 0
→ 𝒃 𝟏 ( 𝒍 𝟏 ) →𝒅
This shaded region thus forms a forbidden range of load admittances that cannot be matched with this particular double-stub tuner.
A simple way of reducing the forbidden range is to reduce the distance d between the stubs.
→ 𝒃 𝟐 ( 𝒍 𝟐 )

17. Smith Chart Solution
𝒛 𝑳 = 𝒁 𝑳 𝒁 𝟎 =𝟏.𝟐−𝒋𝟏.𝟔
𝒚 𝑳 = 𝟏 𝒛 𝑳 =𝟎.𝟑+𝒋𝟎.𝟒

18. Smith Chart Solution
𝑦 𝐿 =0.3+𝑗0.4 ↓
𝑦 1 =0.3+𝑗1.714
𝑦 2 =1−𝑗3.38
𝑦 0 =1
→ 𝒃 𝟏 =𝟏.𝟑𝟏𝟒
→𝒅= 𝝀 𝟖
→ 𝒃 𝟐 =𝟑.𝟑𝟖

19. Smith Chart Solution
Solution 1
Solution 2

20. Range of 𝐺 𝐿 that can be matched
Analytic Solution
𝑌 𝐿 = 𝐺 𝐿 +𝑗 𝐵 𝐿 ↓
𝑌 1 = 𝐺 𝐿 +𝑗 𝐵 1
𝑌 2 = 𝑌 0 +𝑗𝐵
𝑌 0
Real 𝐺 𝐿
∴𝐷𝑒𝑡≥0
Range of 𝐺 𝐿 that can be matched
(5.24 a, b)
(𝑂𝑝𝑒𝑛 𝑠𝑡𝑢𝑏)
(𝑆ℎ𝑜𝑟𝑡𝑒𝑑 𝑠𝑡𝑢𝑏)