Notes 15 ECE 6340 Intermediate EM Waves Fall 2016

Slides:



Advertisements
Similar presentations
Microwave Engineering
Advertisements

Note 2 Transmission Lines (Time Domain)
Microwave Engineering
Uniform plane wave.
Shuichi Noguchi, KEK6-th ILC School, November Shuichi Noguchi, KEK6-th ILC School, November RF Basics; Contents  Maxwell’s Equation  Plane.
Prof. David R. Jackson Dept. of ECE Fall 2013 Notes 15 ECE 6340 Intermediate EM Waves 1.
Prof. David R. Jackson Dept. of ECE Fall 2013 Notes 22 ECE 6340 Intermediate EM Waves 1.
Applied Electricity and Magnetism
Rectangular Waveguides
Prof. David R. Jackson ECE Dept. Fall 2014 Notes 31 ECE 2317 Applied Electricity and Magnetism 1.
Prof. David R. Jackson Notes 19 Waveguiding Structures Waveguiding Structures ECE Spring 2013.
Prof. David R. Jackson Dept. of ECE Fall 2013 Notes 13 ECE 6340 Intermediate EM Waves 1.
Lecture 2. Derive the transmission line parameters (R, L, G, C) in terms of the electromagnetic fields Rederive the telegrapher equations using these.
Lecture 6.
Notes 13 ECE Microwave Engineering
Prof. David R. Jackson ECE Dept. Spring 2014 Notes 12 ECE
Prof. D. R. Wilton Notes 19 Waveguiding Structures Waveguiding Structures ECE 3317 [Chapter 5]
Notes 8 ECE Microwave Engineering Waveguides Part 5:
Prof. David R. Jackson Dept. of ECE Notes 10 ECE Microwave Engineering Fall 2011 Waveguides Part 7: Planar Transmission Lines 1.
Transmission Line Theory
Prof. David R. Jackson Dept. of ECE Fall 2013 Notes 12 ECE 6340 Intermediate EM Waves 1.
Prof. David R. Jackson Dept. of ECE Fall 2013 Notes 9 ECE 6340 Intermediate EM Waves 1.
Rectangular Waveguides
Prof. Ji Chen Notes 6 Transmission Lines (Time Domain) ECE Spring 2014.
Lecture 5.
WAVEGUIDES.
Lecture 2. Review lecture 1 Wavelength: Phase velocity: Characteristic impedance: Kerchhoff’s law Wave equations or Telegraphic equations L, R, C, G ?
8. Wave Guides and Cavities 8A. Wave Guides Suppose we have a region bounded by a conductor We want to consider oscillating fields in the non-conducting.
Prof. David R. Jackson Dept. of ECE Fall 2015 Notes 22 ECE 6340 Intermediate EM Waves 1.
Prof. David R. Jackson ECE Dept. Spring 2016 Notes 10 ECE
Prof. David R. Jackson Dept. of ECE Notes 6 ECE Microwave Engineering Fall 2015 Waveguides Part 3: Attenuation 1.
Prof. David R. Jackson Dept. of ECE Notes 8 ECE Microwave Engineering Fall 2015 Waveguides Part 5: Transverse Equivalent Network (TEN) 1.
ENE 429 Antenna and Transmission lines Theory Lecture 7 Waveguides DATE: 3-5/09/07.
Prof. David R. Jackson Dept. of ECE Fall 2015 Notes 11 ECE 6340 Intermediate EM Waves 1.
Notes 10 ECE Microwave Engineering Waveguides Part 7:
Notes 13 ECE Microwave Engineering
Spring 2015 Notes 25 ECE 6345 Prof. David R. Jackson ECE Dept. 1.
Prof. David R. Jackson Dept. of ECE Fall 2015 Notes 7 ECE 6340 Intermediate EM Waves 1.
ELEC 401 MICROWAVE ELECTRONICS Lecture 6
UPB / ETTI O.DROSU Electrical Engineering 2
Notes 22 ECE 6340 Intermediate EM Waves Fall 2016
Notes 13 ECE 6340 Intermediate EM Waves Fall 2016
Applied Electricity and Magnetism
ECE 6341 Spring 2016 Prof. David R. Jackson ECE Dept. Notes 12.
Notes 5 ECE Microwave Engineering Waveguides Part 2:
Notes 12 ECE 6340 Intermediate EM Waves Fall 2016
Notes 9 ECE 6340 Intermediate EM Waves Fall 2016
Notes 5 ECE Microwave Engineering
ELEC 401 MICROWAVE ELECTRONICS Lecture 6
Notes 14 ECE 6340 Intermediate EM Waves Fall 2016
Microwave Engineering
Microwave Engineering
Microwave Engineering
Microwave Engineering
Notes 7 ECE 6340 Intermediate EM Waves Fall 2016
Notes 18 ECE 6340 Intermediate EM Waves Fall 2016
Microwave Engineering
7e Applied EM by Ulaby and Ravaioli
ECE 6341 Spring 2016 Prof. David R. Jackson ECE Dept. Notes 40.
Applied Electromagnetic Waves Notes 6 Transmission Lines (Time Domain)
Applied Electromagnetic Waves Notes 5 Poynting’s Theorem
Notes 9 Transmission Lines (Frequency Domain)
Applied Electromagnetic Waves Rectangular Waveguides
Applied Electromagnetic Waves Waveguiding Structures
Applied Electromagnetic Waves
Microwave Engineering
7e Applied EM by Ulaby and Ravaioli
ECE 6345 Spring 2015 Prof. David R. Jackson ECE Dept. Notes 4.
ECE 6345 Spring 2015 Prof. David R. Jackson ECE Dept. Notes 27.
4th Week Seminar Sunryul Kim Antennas & RF Devices Lab.
Presentation transcript:

Notes 15 ECE 6340 Intermediate EM Waves Fall 2016 Prof. David R. Jackson Dept. of ECE Notes 15

Attenuation Formula S At z = 0 : At z = Dz : Waveguiding system Waveguiding system (WG or TL): At z = 0 : At z = Dz :

Attenuation Formula (cont.) Hence so If

Attenuation Formula (cont.) S so From conservation of energy: where

Attenuation Formula (cont.) Hence As z  0: Note: Where the point z = 0 is located is arbitrary.

Attenuation Formula (cont.) General formula: This is a perturbational formula for the conductor attenuation. The power flow and power dissipation are usually calculated assuming the fields are those of the mode with PEC conductors. z0

Attenuation on Transmission Line Attenuation due to Conductor Loss The current of the TEM mode flows in the z direction.

Attenuation on Line (cont.) Power dissipation due to conductor loss: Power flowing on line: (Z0 is assumed to be approximately real.) z S A B CA CB I C= CA+ CB

Attenuation on Line (cont.) Hence

R on Transmission Line I Dz R Dz LDz CDz GDz Ignore G for the R calculation ( = c):

R on Transmission Line (cont.) We then have Hence Substituting for ac ,

Total Attenuation on Line Method #1 When we ignore conductor loss to calculate d, we have a TEM mode. so Hence,

Total Attenuation on Line (cont.) Method #2 where The two methods give approximately the same results.

Example: Coax Coaxial Cable z I a A b I B

Example (cont.) Hence Also, Hence (nepers/m)

Example (cont.) Calculate R:

This agrees with the formula obtained from the “DC equivalent model.” Example (cont.) This agrees with the formula obtained from the “DC equivalent model.” (The DC equivalent model assumes that the current is uniform around the boundary, so it is a less general method.) b  a DC equivalent model of coax

Internal Inductance An extra inductance per unit length L is added to the TL model in order to account for the internal inductance of the conductors. This extra (internal) inductance consumes imaginary (reactive) power. The “external inductance” L0 accounts for magnetic energy only in the external region (between the conductors). This is what we get by assuming PEC conductors. Internal inductance R Dz C Dz G Dz DL Dz L0 Dz

Skin Inductance (cont.) Imaginary (reactive) power per meter consumed by the extra inductance: Circuit model: Equate Skin-effect formula: L0 Dz DL Dz R Dz I C Dz G Dz

Skin Inductance (cont.) Hence:

Skin Inductance (cont.) Hence or

Summary of High-Frequency Formulas for Coax Assumption:  << a

Low Frequency (DC) Coax Model At low frequency (DC) we have: Derivation omitted a b c t = c - b

Tesche Model This empirical model combines the low-frequency (DC) and the high-frequency (HF) skin-effect results together into one result by using an approximate circuit model to get R() and L(). F. M. Tesche, “A Simple model for the line parameters of a lossy coaxial cable filled with a nondispersive dielectric,” IEEE Trans. EMC, vol. 49, no. 1, pp. 12-17, Feb. 2007. Note: The method was applied in the above reference for a coaxial cable, but it should work for any type of transmission line. (Please see the Appendix for a discussion of the Tesche model.)

Assume uniform current density on each conductor (h >> a). Twin Lead a x y h Twin Lead Assume uniform current density on each conductor (h >> a). a  x y h DC equivalent model

Twin Lead Twin Lead or y a x h (A more accurate formula will come later.)

Wheeler Incremental Inductance Rule x y A B Wheeler showed that R could be expressed in a way that is easy to calculate (provided we have a formula for L0): L0 is the external inductance (calculated assuming PEC conductors) and n is an increase in the dimension of the conductors (expanded into the active field region). H. Wheeler, "Formulas for the skin-effect," Proc. IRE, vol. 30, pp. 412-424, 1942.

Wheeler Incremental Inductance Rule (cont.) The boundaries are expanded a small amount n into the field region. x y A B Field region n PEC conductors L0 = external inductance (assuming perfect conductors).

Wheeler Incremental Inductance Rule (cont.) Derivation of Wheeler Incremental Inductance rule x y A B Field region (Sext) n PEC conductors Hence We then have

Wheeler Incremental Inductance Rule (cont.) x y A B Field region (Sext) n PEC conductors From the last slide, Hence

Wheeler Incremental Inductance Rule (cont.) Example 1: Coax a b

Wheeler Incremental Inductance Rule (cont.) x y h Example 2: Twin Lead From image theory (or conformal mapping):

Wheeler Incremental Inductance Rule (cont.) x y h Example 2: Twin Lead (cont.) Note: By incrementing a, we increment both conductors simultaneously.

Wheeler Incremental Inductance Rule (cont.) x y h Example 2: Twin Lead (cont.) Summary

Attenuation in Waveguide We consider here conductor loss for a waveguide mode. A waveguide mode is traveling in the positive z direction.

Attenuation in Waveguide (cont.) or Power flow: Next, use Hence

Attenuation in Waveguide (cont.) Vector identity: Hence Assume Z0WG = real ( f > fc and no dielectric loss)

Attenuation in Waveguide (cont.) Then we have S x y C

Attenuation in Waveguide (cont.) Total Attenuation: Calculate d (assume PEC wall): so where

Attenuation in Waveguide (cont.) TE10 Mode

Attenuation in dB z = 0 z S Waveguiding system (WG or TL) Use

Attenuation in dB (cont.) so Hence

Attenuation in dB (cont.) or

Appendix: Tesche Model The series elements Za and Zb (defined on the next slide) account for the finite conductivity, and give us an accurate R and L for each conductor at any frequency. C Za Zb G z L0

Appendix: Tesche Model (cont.) Inner conductor of coax The impedance of this circuit is denoted as Outer conductor of coax The impedance of this circuit is denoted as

Appendix: Tesche Model (cont.) At low frequency the HF resistance gets small and the HF inductance gets large. Inner conductor of coax

Appendix: Tesche Model (cont.) At high frequency the DC inductance gets very large compared to the HF inductance, and the DC resistance is small compared with the HF resistance. Inner conductor of coax

Appendix: Tesche Model (cont.) The formulas are summarized as follows: