Presentation is loading. Please wait.

Presentation is loading. Please wait.

Chapter 4 Microwave Network Analysis

Similar presentations


Presentation on theme: "Chapter 4 Microwave Network Analysis"โ€” Presentation transcript:

1 Chapter 4 Microwave Network Analysis
(4.1 ~ 4.4) ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค

2 4.1 Impedance and Equivalent voltages and current
- Equivalent voltages and currents ๐‘‰= + โˆ’ ๐‘ฌโˆ™๐‘‘๐’ ๐ผ= ๐ถ + ๐‘ฏโˆ™๐‘‘๐’ ์ „์†ก์„ ๋กœ๋ฅผ ๋ถ„์„ํ•  ๋•Œ๋Š” ์ฃผํŒŒ์ˆ˜๊ฐ€ ๋งค์šฐ ๋†’๊ธฐ ๋•Œ๋ฌธ์— ์ผ๋ฐ˜์ ์ธ ํšŒ๋กœ๋ถ„์„๊ณผ๋Š” ๋‹ค๋ฅด๊ฒŒ ํ•ด์„๋จ ๐ธ ๐‘ฆ ๐‘ฅ,๐‘ฆ,๐‘ง = ๐‘—๐œ”๐œ‡๐‘Ž ๐œ‹ ๐ด sin ๐œ‹๐‘ฅ ๐‘Ž ๐‘’ โˆ’๐‘—๐›ฝ๐‘ง =๐ด ๐‘’ ๐‘ฆ ๐‘ฅ,๐‘ฆ ๐‘’ โˆ’๐‘—๐›ฝ๐‘ง ๐ป ๐‘ฅ ๐‘ฅ,๐‘ฆ,๐‘ง = ๐‘—๐›ฝ๐‘Ž ๐œ‹ ๐ด sin ๐œ‹๐‘ฅ ๐‘Ž ๐‘’ โˆ’๐‘—๐›ฝ๐‘ง =๐ด โ„Ž ๐‘ฅ ๐‘ฅ,๐‘ฆ ๐‘’ โˆ’๐‘—๐›ฝ๐‘ง ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค

3 4.1 Impedance and Equivalent voltages and current
- Equivalent voltages and currents ์ „์†ก์„ ๋กœ๋ฅผ ๋ถ„์„ํ•  ๋•Œ๋Š” ์ฃผํŒŒ์ˆ˜๊ฐ€ ๋งค์šฐ ๋†’๊ธฐ ๋•Œ๋ฌธ์— ์ผ๋ฐ˜์ ์ธ ํšŒ๋กœ๋ถ„์„๊ณผ๋Š” ๋‹ค๋ฅด๊ฒŒ ํ•ด์„๋จ ๐‘‰= โˆ’๐‘—๐œ”๐œ‡๐‘Ž ๐œ‹ ๐ด sin ๐œ‹๐‘ฅ ๐‘Ž ๐‘’ โˆ’๐‘—๐›ฝ๐‘ง ๐‘ฆ ๐‘‘๐‘ฆ ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค

4 4.1 Impedance and Equivalent voltages and current
- Equivalent voltages and currents ๐‘ฌ ๐‘ก ๐‘ฅ,๐‘ฆ,๐‘ง =๐’† ๐‘ฅ,๐‘ฆ ๐ด + ๐‘’ โˆ’๐‘—๐›ฝ๐‘ง + ๐ด โˆ’ ๐‘’ ๐‘—๐›ฝ๐‘ง = ๐’† ๐‘ฅ,๐‘ฆ ๐ถ 1 ๐‘‰ + ๐‘’ โˆ’๐‘—๐›ฝ๐‘ง + ๐‘‰ โˆ’ ๐‘’ ๐‘—๐›ฝ๐‘ง ๐‘ฏ ๐‘ก ๐‘ฅ,๐‘ฆ,๐‘ง =๐’‰ ๐‘ฅ,๐‘ฆ ๐ด + ๐‘’ โˆ’๐‘—๐›ฝ๐‘ง + ๐ด โˆ’ ๐‘’ ๐‘—๐›ฝ๐‘ง = ๐’‰ ๐‘ฅ,๐‘ฆ ๐ถ 1 ๐ผ + ๐‘’ โˆ’๐‘—๐›ฝ๐‘ง + ๐ผ โˆ’ ๐‘’ ๐‘—๐›ฝ๐‘ง ๐’‰ ๐‘ฅ,๐‘ฆ = ๐‘ง ร—๐’† ๐‘ฅ,๐‘ฆ ๐‘ ๐œ” ๐‘‰ ๐‘ง = ๐‘‰ + ๐‘’ โˆ’๐‘—๐›ฝ๐‘ง + ๐‘‰ โˆ’ ๐‘’ ๐‘—๐›ฝ๐‘ง ๐ผ ๐‘ง = ๐ผ + ๐‘’ โˆ’๐‘—๐›ฝ๐‘ง โˆ’ ๐ผ โˆ’ ๐‘’ ๐‘—๐›ฝ๐‘ง ์ „์†ก์„ ๋กœ๋ฅผ ๋ถ„์„ํ•  ๋•Œ๋Š” ์ฃผํŒŒ์ˆ˜๊ฐ€ ๋งค์šฐ ๋†’๊ธฐ ๋•Œ๋ฌธ์— ์ผ๋ฐ˜์ ์ธ ํšŒ๋กœ๋ถ„์„๊ณผ๋Š” ๋‹ค๋ฅด๊ฒŒ ํ•ด์„๋จ ๐‘ƒ + = ๐ด ๐‘† ๐’†ร— ๐’‰ โˆ— โˆ™ ๐‘ง ๐‘‘๐‘  = ๐‘‰ + ๐ผ +โˆ— 2 ๐ถ 1 ๐ถ 2 โˆ— ๐‘† ๐’†ร— ๐’‰ โˆ— โˆ™ ๐‘ง ๐‘‘๐‘  ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค

5 4.1 Impedance and Equivalent voltages and current
- Equivalent voltages and currents ๐ถ 1 ๐ถ 2 โˆ— = ๐‘† ๐’†ร— ๐’‰ โˆ— โˆ™ ๐‘ง ๐‘‘๐‘  ๐‘ 0 = ๐‘‰ + ๐ผ + = ๐‘‰ โˆ’ ๐ผ โˆ’ = ๐ถ 1 ๐ถ 2 ๐ถ 1 ๐ถ 2 = ๐‘ ๐œ” ( ๐‘ ๐‘‡๐ธ ๐‘œ๐‘Ÿ ๐‘ ๐‘‡๐‘€ ) ์ „์†ก์„ ๋กœ๋ฅผ ๋ถ„์„ํ•  ๋•Œ๋Š” ์ฃผํŒŒ์ˆ˜๊ฐ€ ๋งค์šฐ ๋†’๊ธฐ ๋•Œ๋ฌธ์— ์ผ๋ฐ˜์ ์ธ ํšŒ๋กœ๋ถ„์„๊ณผ๋Š” ๋‹ค๋ฅด๊ฒŒ ํ•ด์„๋จ ๐‘ฌ ๐‘ก ๐‘ฅ,๐‘ฆ,๐‘ง = ๐‘›=1 ๐‘ ๐‘‰ ๐‘› + ๐ถ 1๐‘› ๐‘’ โˆ’๐‘— ๐›ฝ ๐‘› ๐‘ง + ๐‘‰ ๐‘› โˆ’ ๐ถ 1๐‘› ๐‘’ ๐‘— ๐›ฝ ๐‘› ๐‘ง ๐’† ๐‘› ๐‘ฅ,๐‘ฆ ๐‘ฏ ๐‘ก ๐‘ฅ,๐‘ฆ,๐‘ง = ๐‘›=1 ๐‘ ๐ผ ๐‘› + ๐ถ 2๐‘› ๐‘’ โˆ’๐‘— ๐›ฝ ๐‘› ๐‘ง + ๐ผ ๐‘› โˆ’ ๐ถ 2๐‘› ๐‘’ ๐‘— ๐›ฝ ๐‘› ๐‘ง ๐’‰ ๐‘› ๐‘ฅ,๐‘ฆ ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค

6 4.1 Impedance and Equivalent voltages and current
- The concept of impedance name equation character Intrinsic impedance ๐œ‚= ๐œ‡/๐œ– Depend on only the material parameters of the medium Equal to the wave impedance for plane waves Wave impedance ๐‘ ๐‘ค = ๐ธ ๐‘ก ๐ป ๐‘ก = 1 ๐‘Œ ๐‘ค TEM, TM, TE waves each have different wave impedances Depend on line or guide, the material, and the operation frequency Characteristic impedance ๐‘ 0 = 1 ๐‘Œ 0 = ๐‘‰ + ๐ผ + Ratio of voltage to current for a traveling wave on a transmission line Characteristic impedance of a TEM wave is unique ์ „์†ก์„ ๋กœ๋ฅผ ๋ถ„์„ํ•  ๋•Œ๋Š” ์ฃผํŒŒ์ˆ˜๊ฐ€ ๋งค์šฐ ๋†’๊ธฐ ๋•Œ๋ฌธ์— ์ผ๋ฐ˜์ ์ธ ํšŒ๋กœ๋ถ„์„๊ณผ๋Š” ๋‹ค๋ฅด๊ฒŒ ํ•ด์„๋จ ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค

7 4.1 Impedance and Equivalent voltages and current
- The concept of impedance ๐‘ƒ= 1 2 ๐‘† ๐‘ฌร— ๐‘ฏ โˆ— โˆ™๐‘‘๐’” = ๐‘ƒ ๐‘™ +2๐‘—๐œ” ๐‘Š ๐‘š โˆ’ ๐‘Š ๐‘’ ๐‘ฌ ๐‘ก ๐‘ฅ,๐‘ฆ,๐‘ง =๐‘‰ ๐‘ง ๐’† ๐‘ฅ,๐‘ฆ ๐‘’ โˆ’๐‘—๐›ฝ๐‘ง ๐‘ฏ ๐‘ก ๐‘ฅ,๐‘ฆ,๐‘ง =๐ผ ๐‘ง ๐’‰ ๐‘ฅ,๐‘ฆ ๐‘’ โˆ’๐‘—๐›ฝ๐‘ง ๐‘† ๐’†ร—๐’‰โˆ™๐‘‘๐’” =1 ์ „์†ก์„ ๋กœ๋ฅผ ๋ถ„์„ํ•  ๋•Œ๋Š” ์ฃผํŒŒ์ˆ˜๊ฐ€ ๋งค์šฐ ๋†’๊ธฐ ๋•Œ๋ฌธ์— ์ผ๋ฐ˜์ ์ธ ํšŒ๋กœ๋ถ„์„๊ณผ๋Š” ๋‹ค๋ฅด๊ฒŒ ํ•ด์„๋จ ๐‘ƒ= 1 2 ๐‘† ๐‘‰ ๐ผ โˆ— ๐’†ร—๐’‰โˆ™๐‘‘๐’” = 1 2 ๐‘‰ ๐ผ โˆ— ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค

8 4.1 Impedance and Equivalent voltages and current
- The concept of impedance ๐‘ ๐‘–๐‘› =๐‘…+๐‘—๐‘‹= ๐‘‰ ๐ผ = ๐‘ƒ ๐ผ 2 = ๐‘ƒ ๐‘™ +2๐‘—๐œ”( ๐‘Š ๐‘š โˆ’ ๐‘Š ๐‘’ ) ๐ผ 2 ๐‘‹= 4๐œ” ๐‘Š ๐‘š โˆ’ ๐‘Š ๐‘’ ๐ผ 2 ์ „์†ก์„ ๋กœ๋ฅผ ๋ถ„์„ํ•  ๋•Œ๋Š” ์ฃผํŒŒ์ˆ˜๊ฐ€ ๋งค์šฐ ๋†’๊ธฐ ๋•Œ๋ฌธ์— ์ผ๋ฐ˜์ ์ธ ํšŒ๋กœ๋ถ„์„๊ณผ๋Š” ๋‹ค๋ฅด๊ฒŒ ํ•ด์„๋จ ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค

9 4.1 Impedance and Equivalent voltages and current
- Even and Odd Properties of ๐‘ ๐œ” and ฮ“ ๐œ” ๐‘ฃ ๐‘ก = 1 2๐œ‹ โˆ’โˆž โˆž ๐‘‰ ๐œ” ๐‘’ ๐‘—๐œ”๐‘ก ๐‘‘๐œ” ๐‘‰ โˆ’๐œ” = ๐‘‰ โˆ— ๐œ” ์ „์†ก์„ ๋กœ๋ฅผ ๋ถ„์„ํ•  ๋•Œ๋Š” ์ฃผํŒŒ์ˆ˜๊ฐ€ ๋งค์šฐ ๋†’๊ธฐ ๋•Œ๋ฌธ์— ์ผ๋ฐ˜์ ์ธ ํšŒ๋กœ๋ถ„์„๊ณผ๋Š” ๋‹ค๋ฅด๊ฒŒ ํ•ด์„๋จ ๐‘‰ โˆ— ๐œ” = ๐‘ โˆ— โˆ’๐œ” ๐ผ โˆ— โˆ’๐œ” = ๐‘ โˆ— โˆ’๐œ” ๐ผ ๐œ” =๐‘‰ ๐œ” =๐‘ ๐œ” ๐ผ ๐œ” ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค

10 4.1 Impedance and Equivalent voltages and current
- Even and Odd Properties of ๐‘ ๐œ” and ฮ“ ๐œ” ฮ“ ๐œ” = ๐‘ ๐œ” โˆ’ ๐‘ 0 ๐‘ ๐œ” + ๐‘ 0 = ๐‘… ๐œ” โˆ’ ๐‘ 0 +๐‘—๐‘‹ ๐œ” ๐‘… ๐œ” + ๐‘ 0 +๐‘—๐‘‹ ๐œ” ฮ“ โˆ’๐œ” = ๐‘… ๐œ” โˆ’ ๐‘ 0 โˆ’๐‘—๐‘‹ ๐œ” ๐‘… ๐œ” + ๐‘ 0 โˆ’๐‘—๐‘‹ ๐œ” = ฮ“ โˆ— ๐œ” ์ „์†ก์„ ๋กœ๋ฅผ ๋ถ„์„ํ•  ๋•Œ๋Š” ์ฃผํŒŒ์ˆ˜๊ฐ€ ๋งค์šฐ ๋†’๊ธฐ ๋•Œ๋ฌธ์— ์ผ๋ฐ˜์ ์ธ ํšŒ๋กœ๋ถ„์„๊ณผ๋Š” ๋‹ค๋ฅด๊ฒŒ ํ•ด์„๋จ ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค

11 4.2 Impedance and Admittance matrices
๐‘‰ ๐‘› = ๐‘‰ ๐‘› + + ๐‘‰ ๐‘› โˆ’ ๐ผ ๐‘› = ๐ผ ๐‘› + โˆ’ ๐ผ ๐‘› โˆ’ ์ „์†ก์„ ๋กœ๋ฅผ ๋ถ„์„ํ•  ๋•Œ๋Š” ์ฃผํŒŒ์ˆ˜๊ฐ€ ๋งค์šฐ ๋†’๊ธฐ ๋•Œ๋ฌธ์— ์ผ๋ฐ˜์ ์ธ ํšŒ๋กœ๋ถ„์„๊ณผ๋Š” ๋‹ค๋ฅด๊ฒŒ ํ•ด์„๋จ ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค

12 4.2 Impedance and Admittance matrices
๐‘‰ 1 ๐‘‰ 2 โ‹ฎ ๐‘‰ ๐‘ = ๐‘ 11 โ‹ฏ ๐‘ 1๐‘ โ‹ฎ โ‹ฑ โ‹ฎ ๐‘ ๐‘1 โ‹ฏ ๐‘ ๐‘๐‘ ๐ผ 1 ๐ผ 2 โ‹ฎ ๐ผ ๐‘ ๐‘‰ = ๐‘ ๐ผ ๐ผ 1 ๐ผ 2 โ‹ฎ ๐ผ ๐‘ = ๐‘Œ 11 โ‹ฏ ๐‘Œ 1๐‘ โ‹ฎ โ‹ฑ โ‹ฎ ๐‘Œ ๐‘1 โ‹ฏ ๐‘Œ ๐‘๐‘ ๐‘‰ 1 ๐‘‰ 2 โ‹ฎ ๐‘‰ ๐‘ ๐ผ = ๐‘Œ ๐‘‰ ๐‘ ๐‘–๐‘— = ๐‘‰ ๐‘– ๐ผ ๐‘— โ€‹ ๐ผ ๐‘˜ =0 ๐‘“๐‘œ๐‘Ÿ ๐‘˜โ‰ ๐‘— ๐‘Œ ๐‘–๐‘— = ๐ผ ๐‘– ๐‘‰ ๐‘— โ€‹ ๐‘‰ ๐‘˜ =0 ๐‘“๐‘œ๐‘Ÿ ๐‘˜โ‰ ๐‘— ์ „์†ก์„ ๋กœ๋ฅผ ๋ถ„์„ํ•  ๋•Œ๋Š” ์ฃผํŒŒ์ˆ˜๊ฐ€ ๋งค์šฐ ๋†’๊ธฐ ๋•Œ๋ฌธ์— ์ผ๋ฐ˜์ ์ธ ํšŒ๋กœ๋ถ„์„๊ณผ๋Š” ๋‹ค๋ฅด๊ฒŒ ํ•ด์„๋จ ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค

13 4.2 Impedance and Admittance matrices
- Reciprocal networks ๐‘† ๐‘ฌ ๐‘Ž ร— ๐‘ฏ ๐‘ โˆ™๐‘‘๐’”= ๐‘† ๐‘ฌ ๐‘ ร— ๐‘ฏ ๐‘Ž โˆ™๐‘‘๐’” ๐‘ฌ 1๐‘Ž = ๐‘ฝ 1๐‘Ž ๐’† 1 , ๐‘ฏ 1๐‘Ž = ๐‘ฐ 1๐‘Ž ๐’‰ 1 ๐‘ฌ 1๐‘ = ๐‘ฝ 1๐‘ ๐’† 1 , ๐‘ฏ 1๐‘ = ๐‘ฐ 1๐‘ ๐’‰ 1 ๐‘ฌ 2๐‘Ž = ๐‘ฝ 2๐‘Ž ๐’† 2 , ๐‘ฏ 2๐‘Ž = ๐‘ฐ 2๐‘Ž ๐’‰ 2 ๐‘ฌ 2๐‘ = ๐‘ฝ 2๐‘ ๐’† 2 , ๐‘ฏ 2๐‘ = ๐‘ฐ 2๐‘ ๐’‰ 2 ๐‘‰ 1๐‘Ž ๐ผ 1๐‘ โˆ’ ๐‘‰ 1๐‘ ๐ผ 1๐‘Ž ๐‘† 1 ๐’† 1 ร— ๐’‰ 1 โˆ™๐‘‘๐’” + ๐‘‰ 2๐‘Ž ๐ผ 2๐‘ โˆ’ ๐‘‰ 2๐‘ ๐ผ 2๐‘Ž ๐‘† 2 ๐’† 2 ร— ๐’‰ 2 โˆ™๐‘‘๐’” =0 ์ „์†ก์„ ๋กœ๋ฅผ ๋ถ„์„ํ•  ๋•Œ๋Š” ์ฃผํŒŒ์ˆ˜๊ฐ€ ๋งค์šฐ ๋†’๊ธฐ ๋•Œ๋ฌธ์— ์ผ๋ฐ˜์ ์ธ ํšŒ๋กœ๋ถ„์„๊ณผ๋Š” ๋‹ค๋ฅด๊ฒŒ ํ•ด์„๋จ ๐‘† 1 ๐’† 1 ร— ๐’‰ 1 โˆ™๐‘‘๐’” = ๐‘† 2 ๐’† 2 ร— ๐’‰ 2 โˆ™๐‘‘๐’” =1 ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค

14 4.2 Impedance and Admittance matrices
- Reciprocal networks ๐‘‰ 1๐‘Ž ๐ผ 1๐‘ โˆ’ ๐‘‰ 1๐‘ ๐ผ 1๐‘Ž + ๐‘‰ 2๐‘Ž ๐ผ 2๐‘ โˆ’ ๐‘‰ 2๐‘ ๐ผ 2๐‘Ž =0 ๐ผ 1 = ๐‘Œ 11 ๐‘‰ 1 + ๐‘Œ 12 ๐‘‰ 2 ๐ผ 2 = ๐‘Œ 21 ๐‘‰ 1 + ๐‘Œ 22 ๐‘‰ 2 ๐‘‰ 1๐‘Ž ๐‘‰ 2๐‘ โˆ’ ๐‘‰ 1๐‘ ๐‘‰ 2๐‘Ž ๐‘Œ 12 โˆ’ ๐‘Œ 21 =0 ์ „์†ก์„ ๋กœ๋ฅผ ๋ถ„์„ํ•  ๋•Œ๋Š” ์ฃผํŒŒ์ˆ˜๊ฐ€ ๋งค์šฐ ๋†’๊ธฐ ๋•Œ๋ฌธ์— ์ผ๋ฐ˜์ ์ธ ํšŒ๋กœ๋ถ„์„๊ณผ๋Š” ๋‹ค๋ฅด๊ฒŒ ํ•ด์„๋จ ๐‘Œ ๐‘–๐‘— = ๐‘Œ ๐‘—๐‘– ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค

15 4.2 Impedance and Admittance matrices
- Lossless networks ๐‘ƒ ๐‘Ž๐‘ฃ๐‘” = ๐‘‰ ๐‘ก ๐ผ โˆ— = ๐‘ ๐ผ ๐‘ก ๐ผ โˆ— = ๐ผ ๐‘ก ๐‘ ๐ผ โˆ— = ๐ผ 1 ๐‘ 11 ๐ผ 1 โˆ— + ๐ผ 1 ๐‘ 12 ๐ผ 2 โˆ— + ๐ผ 2 ๐‘ 21 ๐ผ 1 โˆ— +โ‹ฏ = 1 2 ๐‘›=1 ๐‘ ๐‘š=1 ๐‘ ๐ผ ๐‘š ๐‘ ๐‘š๐‘› ๐ผ ๐‘› โˆ— ๐‘…๐‘’ ๐‘ƒ ๐‘Ž๐‘ฃ๐‘” =0 ๐‘…๐‘’ ๐‘ ๐‘›๐‘› =0 ์ „์†ก์„ ๋กœ๋ฅผ ๋ถ„์„ํ•  ๋•Œ๋Š” ์ฃผํŒŒ์ˆ˜๊ฐ€ ๋งค์šฐ ๋†’๊ธฐ ๋•Œ๋ฌธ์— ์ผ๋ฐ˜์ ์ธ ํšŒ๋กœ๋ถ„์„๊ณผ๋Š” ๋‹ค๋ฅด๊ฒŒ ํ•ด์„๋จ ๐‘…๐‘’ ๐ผ ๐‘› ๐ผ ๐‘š โˆ— + ๐ผ ๐‘š ๐ผ ๐‘› โˆ— ๐‘ ๐‘š๐‘› =0 ๐‘…๐‘’ ๐‘ ๐‘š๐‘› =0 ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค

16 4.3 The scattering matrix ๐‘‰ 1 โˆ’ ๐‘‰ 2 โˆ’ โ‹ฎ ๐‘‰ ๐‘ โˆ’ = ๐‘† 11 โ‹ฏ ๐‘† 1๐‘ โ‹ฎ โ‹ฑ โ‹ฎ ๐‘† ๐‘1 โ‹ฏ ๐‘† ๐‘๐‘ ๐‘‰ ๐‘‰ 2 + โ‹ฎ ๐‘‰ ๐‘ + ๐‘‰ โˆ’ = ๐‘† ๐‘‰ + ๐‘† ๐‘–๐‘— = ๐‘‰ ๐‘– โˆ’ ๐‘‰ ๐‘— + โ€‹ ๐‘‰ ๐‘˜ =0 ๐‘“๐‘œ๐‘Ÿ ๐‘˜โ‰ ๐‘— ์ „์†ก์„ ๋กœ๋ฅผ ๋ถ„์„ํ•  ๋•Œ๋Š” ์ฃผํŒŒ์ˆ˜๊ฐ€ ๋งค์šฐ ๋†’๊ธฐ ๋•Œ๋ฌธ์— ์ผ๋ฐ˜์ ์ธ ํšŒ๋กœ๋ถ„์„๊ณผ๋Š” ๋‹ค๋ฅด๊ฒŒ ํ•ด์„๋จ ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค

17 4.3 The scattering matrix - Relationships both Z and S ๐‘ 0๐‘› =1
๐‘‰ ๐‘› = ๐‘‰ ๐‘› + + ๐‘‰ ๐‘› โˆ’ ๐ผ ๐‘› = ๐ผ ๐‘› + โˆ’ ๐ผ ๐‘› โˆ’ = ๐‘‰ ๐‘› + โˆ’ ๐‘‰ ๐‘› โˆ’ ์ „์†ก์„ ๋กœ๋ฅผ ๋ถ„์„ํ•  ๋•Œ๋Š” ์ฃผํŒŒ์ˆ˜๊ฐ€ ๋งค์šฐ ๋†’๊ธฐ ๋•Œ๋ฌธ์— ์ผ๋ฐ˜์ ์ธ ํšŒ๋กœ๋ถ„์„๊ณผ๋Š” ๋‹ค๋ฅด๊ฒŒ ํ•ด์„๋จ ๐‘ ๐ผ = ๐‘ ๐‘‰ + โˆ’ ๐‘ ๐‘‰ โˆ’ = ๐‘‰ = ๐‘‰ ๐‘‰ โˆ’ ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค

18 4.3 The scattering matrix - Relationships both Z and S
๐‘ + ๐‘ˆ ๐‘‰ โˆ’ = ๐‘ โˆ’ ๐‘ˆ ๐‘‰ + ๐‘† = ๐‘ + ๐‘ˆ โˆ’1 ๐‘ โˆ’ ๐‘ˆ ๐‘ = ๐‘ˆ + ๐‘† ๐‘ˆ โˆ’ ๐‘† โˆ’1 ์ „์†ก์„ ๋กœ๋ฅผ ๋ถ„์„ํ•  ๋•Œ๋Š” ์ฃผํŒŒ์ˆ˜๊ฐ€ ๋งค์šฐ ๋†’๊ธฐ ๋•Œ๋ฌธ์— ์ผ๋ฐ˜์ ์ธ ํšŒ๋กœ๋ถ„์„๊ณผ๋Š” ๋‹ค๋ฅด๊ฒŒ ํ•ด์„๋จ ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค

19 4.3 The scattering matrix - Reciprocal networks and Lossless networks
๐‘‰ ๐‘› + = 1 2 ( ๐‘‰ ๐‘› + ๐ผ ๐‘› ) ๐‘‰ + = ๐‘ + ๐‘ˆ ๐ผ ๐‘‰ ๐‘› โˆ’ = 1 2 ( ๐‘‰ ๐‘› โˆ’ ๐ผ ๐‘› ) ๐‘‰ โˆ’ = ๐‘ โˆ’ ๐‘ˆ ๐ผ ์ „์†ก์„ ๋กœ๋ฅผ ๋ถ„์„ํ•  ๋•Œ๋Š” ์ฃผํŒŒ์ˆ˜๊ฐ€ ๋งค์šฐ ๋†’๊ธฐ ๋•Œ๋ฌธ์— ์ผ๋ฐ˜์ ์ธ ํšŒ๋กœ๋ถ„์„๊ณผ๋Š” ๋‹ค๋ฅด๊ฒŒ ํ•ด์„๋จ ๐‘‰ โˆ’ = ๐‘ โˆ’ ๐‘ˆ ๐‘ + ๐‘ˆ โˆ’1 ๐‘‰ + ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค

20 4.3 The scattering matrix - Reciprocal networks and Lossless networks
๐‘† = ๐‘ โˆ’ ๐‘ˆ ๐‘ + ๐‘ˆ โˆ’1 ๐‘† ๐‘ก = ๐‘ + ๐‘ˆ โˆ’1 ๐‘ โˆ’ ๐‘ˆ ๐‘† = ๐‘† ๐‘ก ์ „์†ก์„ ๋กœ๋ฅผ ๋ถ„์„ํ•  ๋•Œ๋Š” ์ฃผํŒŒ์ˆ˜๊ฐ€ ๋งค์šฐ ๋†’๊ธฐ ๋•Œ๋ฌธ์— ์ผ๋ฐ˜์ ์ธ ํšŒ๋กœ๋ถ„์„๊ณผ๋Š” ๋‹ค๋ฅด๊ฒŒ ํ•ด์„๋จ ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค

21 4.3 The scattering matrix - Reciprocal networks and Lossless networks
๐‘ƒ ๐‘Ž๐‘ฃ๐‘” = 1 2 ๐‘…๐‘’ ๐‘‰ ๐‘ก ๐ผ โˆ— = 1 2 ๐‘…๐‘’ ๐‘‰ + ๐‘ก + ๐‘‰ โˆ’ ๐‘ก ๐‘‰ + โˆ— โˆ’ ๐‘‰ โˆ’ โˆ— = ๐‘‰ + ๐‘ก ๐‘‰ + โˆ— โˆ’ ๐‘‰ โˆ’ ๐‘ก ๐‘‰ โˆ’ โˆ— =0 ๐‘‰ + ๐‘ก ๐‘‰ + โˆ— = ๐‘‰ โˆ’ ๐‘ก ๐‘‰ โˆ’ โˆ— = ๐‘‰ + ๐‘ก ๐‘† ๐‘ก ๐‘† โˆ— ๐‘‰ + โˆ— ์ „์†ก์„ ๋กœ๋ฅผ ๋ถ„์„ํ•  ๋•Œ๋Š” ์ฃผํŒŒ์ˆ˜๊ฐ€ ๋งค์šฐ ๋†’๊ธฐ ๋•Œ๋ฌธ์— ์ผ๋ฐ˜์ ์ธ ํšŒ๋กœ๋ถ„์„๊ณผ๋Š” ๋‹ค๋ฅด๊ฒŒ ํ•ด์„๋จ ๐‘† ๐‘ก ๐‘† โˆ— = ๐‘ˆ ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค

22 4.3 The scattering matrix - A shift in reference planes ๐‘‰ โˆ’ = ๐‘† ๐‘‰ +
์ „์†ก์„ ๋กœ๋ฅผ ๋ถ„์„ํ•  ๋•Œ๋Š” ์ฃผํŒŒ์ˆ˜๊ฐ€ ๋งค์šฐ ๋†’๊ธฐ ๋•Œ๋ฌธ์— ์ผ๋ฐ˜์ ์ธ ํšŒ๋กœ๋ถ„์„๊ณผ๋Š” ๋‹ค๋ฅด๊ฒŒ ํ•ด์„๋จ ๐‘‰ โˆ’ = ๐‘† ๐‘‰ + ๐‘‰โ€ฒ โˆ’ = ๐‘†โ€ฒ ๐‘‰โ€ฒ + ๐‘‰ ๐‘› โ€ฒ + = ๐‘‰ ๐‘› + ๐‘’ ๐‘— ๐œƒ ๐‘› ๐‘‰ ๐‘› โ€ฒ โˆ’ = ๐‘‰ ๐‘› โˆ’ ๐‘’ โˆ’๐‘— ๐œƒ ๐‘› ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค

23 4.3 The scattering matrix - A shift in reference planes
๐‘’ ๐‘— ๐œƒ 1 โ‹ฏ 0 โ‹ฎ โ‹ฑ โ‹ฎ 0 โ‹ฏ ๐‘’ ๐‘— ๐œƒ ๐‘ ๐‘‰ โ€ฒโˆ’ = ๐‘† ๐‘’ โˆ’๐‘— ๐œƒ 1 โ‹ฏ 0 โ‹ฎ โ‹ฑ โ‹ฎ 0 โ‹ฏ ๐‘’ โˆ’๐‘— ๐œƒ ๐‘ ๐‘‰ โ€ฒ+ ๐‘‰ โ€ฒโˆ’ = ๐‘’ ๐‘— ๐œƒ 1 โ‹ฏ 0 โ‹ฎ โ‹ฑ โ‹ฎ 0 โ‹ฏ ๐‘’ ๐‘— ๐œƒ ๐‘ ๐‘† ๐‘’ โˆ’๐‘— ๐œƒ 1 โ‹ฏ 0 โ‹ฎ โ‹ฑ โ‹ฎ 0 โ‹ฏ ๐‘’ โˆ’๐‘— ๐œƒ ๐‘ ๐‘‰ โ€ฒ+ ์ „์†ก์„ ๋กœ๋ฅผ ๋ถ„์„ํ•  ๋•Œ๋Š” ์ฃผํŒŒ์ˆ˜๊ฐ€ ๋งค์šฐ ๋†’๊ธฐ ๋•Œ๋ฌธ์— ์ผ๋ฐ˜์ ์ธ ํšŒ๋กœ๋ถ„์„๊ณผ๋Š” ๋‹ค๋ฅด๊ฒŒ ํ•ด์„๋จ ๐‘†โ€ฒ = ๐‘’ ๐‘— ๐œƒ 1 โ‹ฏ 0 โ‹ฎ โ‹ฑ โ‹ฎ 0 โ‹ฏ ๐‘’ ๐‘— ๐œƒ ๐‘ ๐‘† ๐‘’ โˆ’๐‘— ๐œƒ 1 โ‹ฏ 0 โ‹ฎ โ‹ฑ โ‹ฎ 0 โ‹ฏ ๐‘’ โˆ’๐‘— ๐œƒ ๐‘ ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค

24 4.3 The scattering matrix - Power waves and generalized scattering parameters ๐‘Ž= ๐‘‰+ ๐‘ ๐‘… ๐ผ 2 ๐‘… ๐‘… ๐‘= ๐‘‰โˆ’ ๐‘ ๐‘… โˆ— ๐ผ 2 ๐‘… ๐‘… ์ „์†ก์„ ๋กœ๋ฅผ ๋ถ„์„ํ•  ๋•Œ๋Š” ์ฃผํŒŒ์ˆ˜๊ฐ€ ๋งค์šฐ ๋†’๊ธฐ ๋•Œ๋ฌธ์— ์ผ๋ฐ˜์ ์ธ ํšŒ๋กœ๋ถ„์„๊ณผ๋Š” ๋‹ค๋ฅด๊ฒŒ ํ•ด์„๋จ Where (reference impedance ๐‘ ๐‘… = ๐‘… ๐‘… +๐‘— ๐‘‹ ๐‘… ) ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค

25 4.3 The scattering matrix - Power waves and generalized scattering parameters ๐‘‰= ๐‘ ๐‘… โˆ— ๐‘Ž+ ๐‘ ๐‘… ๐‘ ๐‘… ๐‘… ๐ผ= ๐‘Žโˆ’๐‘ ๐‘… ๐‘… ๐‘ƒ ๐ฟ = 1 2 ๐‘…๐‘’ ๐‘‰ ๐ผ โˆ— = 1 2 ๐‘… ๐‘… ๐‘…๐‘’ ๐‘ ๐‘… โˆ— ๐‘Ž 2 โˆ’ ๐‘ ๐‘… โˆ— ๐‘Ž ๐‘ โˆ— + ๐‘ ๐‘… ๐‘Ž โˆ— ๐‘โˆ’ ๐‘ ๐‘… ๐‘ 2 = ๐‘Ž 2 โˆ’ ๐‘ 2 ์ „์†ก์„ ๋กœ๋ฅผ ๋ถ„์„ํ•  ๋•Œ๋Š” ์ฃผํŒŒ์ˆ˜๊ฐ€ ๋งค์šฐ ๋†’๊ธฐ ๋•Œ๋ฌธ์— ์ผ๋ฐ˜์ ์ธ ํšŒ๋กœ๋ถ„์„๊ณผ๋Š” ๋‹ค๋ฅด๊ฒŒ ํ•ด์„๋จ ฮ“ ๐‘ = ๐‘ ๐‘Ž = ๐‘‰โˆ’ ๐‘ ๐‘… โˆ— ๐ผ ๐‘‰+ ๐‘ ๐‘… โˆ— ๐ผ = ๐‘ ๐ฟ โˆ’ ๐‘ ๐‘… โˆ— ๐‘ ๐ฟ + ๐‘ ๐‘… โˆ— ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค

26 4.3 The scattering matrix - Power waves and generalized scattering parameters ๐‘ ๐‘… = ๐‘ ๐ฟ โˆ— ๐‘‰= ๐‘‰ 0 ๐‘ ๐ฟ ๐‘ ๐ฟ + ๐‘ ๐‘” ,๐ผ= ๐‘‰ 0 ๐‘ ๐ฟ + ๐‘ ๐‘” , ๐‘ƒ ๐ฟ = ๐‘‰ ๐‘… ๐ฟ ๐‘ ๐ฟ + ๐‘ ๐‘” 2 ๐‘Ž= ๐‘‰ ๐‘… ๐ฟ ๐‘ ๐ฟ + ๐‘ ๐‘” , ๐‘=0 ์ „์†ก์„ ๋กœ๋ฅผ ๋ถ„์„ํ•  ๋•Œ๋Š” ์ฃผํŒŒ์ˆ˜๊ฐ€ ๋งค์šฐ ๋†’๊ธฐ ๋•Œ๋ฌธ์— ์ผ๋ฐ˜์ ์ธ ํšŒ๋กœ๋ถ„์„๊ณผ๋Š” ๋‹ค๋ฅด๊ฒŒ ํ•ด์„๋จ ๐‘ƒ ๐ฟ = ๐‘Ž 2 = ๐‘‰ ๐‘… ๐ฟ ๐‘ ๐ฟ + ๐‘ ๐‘” 2 ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค

27 4.3 The scattering matrix - Power waves and generalized scattering parameters ๐‘Ž = ๐น ๐‘‰ + ๐‘ ๐‘… ๐ผ ๐‘ = ๐น ๐‘‰ โˆ’ ๐‘ ๐‘… โˆ— ๐ผ ๐น = 1 2 ๐‘…๐‘’ ๐‘ ๐‘…๐‘– ์ „์†ก์„ ๋กœ๋ฅผ ๋ถ„์„ํ•  ๋•Œ๋Š” ์ฃผํŒŒ์ˆ˜๊ฐ€ ๋งค์šฐ ๋†’๊ธฐ ๋•Œ๋ฌธ์— ์ผ๋ฐ˜์ ์ธ ํšŒ๋กœ๋ถ„์„๊ณผ๋Š” ๋‹ค๋ฅด๊ฒŒ ํ•ด์„๋จ ๐‘† ๐‘ = ๐น ๐‘ โˆ’ ๐‘ ๐‘… โˆ— ๐‘ + ๐‘ ๐‘… โˆ’1 ๐น โˆ’1 ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค

28 4.4 The transmission (ABCD) matrix
์ „์†ก์„ ๋กœ๋ฅผ ๋ถ„์„ํ•  ๋•Œ๋Š” ์ฃผํŒŒ์ˆ˜๊ฐ€ ๋งค์šฐ ๋†’๊ธฐ ๋•Œ๋ฌธ์— ์ผ๋ฐ˜์ ์ธ ํšŒ๋กœ๋ถ„์„๊ณผ๋Š” ๋‹ค๋ฅด๊ฒŒ ํ•ด์„๋จ ๐‘‰ 1 ๐ผ 1 = ๐ด ๐ต ๐ถ ๐ท ๐‘‰ 2 ๐ผ 2 ๐‘‰ 1 ๐ผ 1 = ๐ด 1 ๐ต 1 ๐ถ 1 ๐ท ๐ด 2 ๐ต 2 ๐ถ 2 ๐ท ๐‘‰ 3 ๐ผ 3 ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค

29 4.4 The transmission (ABCD) matrix
์ „์†ก์„ ๋กœ๋ฅผ ๋ถ„์„ํ•  ๋•Œ๋Š” ์ฃผํŒŒ์ˆ˜๊ฐ€ ๋งค์šฐ ๋†’๊ธฐ ๋•Œ๋ฌธ์— ์ผ๋ฐ˜์ ์ธ ํšŒ๋กœ๋ถ„์„๊ณผ๋Š” ๋‹ค๋ฅด๊ฒŒ ํ•ด์„๋จ ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค

30 4.4 The transmission (ABCD) matrix
์ „์†ก์„ ๋กœ๋ฅผ ๋ถ„์„ํ•  ๋•Œ๋Š” ์ฃผํŒŒ์ˆ˜๊ฐ€ ๋งค์šฐ ๋†’๊ธฐ ๋•Œ๋ฌธ์— ์ผ๋ฐ˜์ ์ธ ํšŒ๋กœ๋ถ„์„๊ณผ๋Š” ๋‹ค๋ฅด๊ฒŒ ํ•ด์„๋จ ์ „์žํŒŒ์—ฐ๊ตฌ์‹ค


Download ppt "Chapter 4 Microwave Network Analysis"

Similar presentations


Ads by Google