Transmission Lines
Content
Characteristic Impedance
Characteristic impedance corresponds to the input impedance of a uniform transmission line of infinite length, i.e., Zin = Vi /II It also corresponds to the input impedance of a transmission line of finite length that is terminated in its own characteristic impedance. In general, the characteristic impedance is a complex number with a resistive and reactive component. It is a function of the frequency of the applied signal, and is unrelated to length. At very high frequencies, the characteristic impedance asymptotes to a fixed value which is resistive. For example, coaxial cables have an impedance of 50 or 75 Ohms at high frequencies. Typically, twisted-pair telephone cables have an impedance of 100 Ohms above 1 MHz. Characteristic impedance is of prime importance for good transmission. Maximum power transfer occurs when the source has the same impedance as the load. Thus for sending signals over a line, the transmitting equipment must have the same characteristic impedance as the line to get the maximum signal into the line. At the other end of the line, the receiving equipment must also have the same impedance as the line to be able to get the maximum signal out of the line. Where impedances do not match, some of the signal is reflected back towards the source. In many cases this reflected signal causes problems and is therefore undesirable. The formulae for characteristic impedance are:
Characteristic impedance changes considerably with frequency, particularly from DC to about 100 kHz. Simplified formula may be derived from the one above. At DC ( 0kHz)
At voice frequencies (eg 1kHz)
At high frequencies (> 100 kHz)
For twisted pair and coaxial cables, the resistance is determined by the diameter or weight of copper, the inductance is very small, and the shunt conductance is small. The major influence on characteristic impedance and other secondary coefficients is the capacitance. This is largely determined by the type of insulation (dielectric) used. Characteristic impedance, for high frequencies, can be stated in terms of the physical dimensions of the cable. These formulae apply to copper conductor cables:
For twisted pair:
For coaxial cable:
These formulae show that the characteristic impedance of any cable is directly determined by the conductor sizes, the spacing between them and the type of insulation used. Any change in these will affect the characteristic impedance.
General Cable New Zealand HEAD OFFICE 75-89 Main South Rd PO Box 8044 Riccarton Christchurch Ph: (03) 348 5199 Fax: (03) 348 2009 Website: www. generalcable.co.nz
General Cable Australia Pty Ltd Sales: 1300 363 282 Fax: 1300 363 382 www.generalcable.com.au
Diagrams of cables are illustrative only and are not necessarily to scale. This brochure is distributed with the understanding that the authors and editors are not responsible for the results of any actions taken on the basis of information in this work , or any errors or omissions. Further, General Cable is not engaged in rendering professional services. General Cable expressly disclaims all and any liability to any person in respect of anything and of the consequences of anything done or omitted to be done by any such person in reliance whether whole or partial of the whole or any of the contents of this publication. All rights reserved. No part of this work covered by copyright may be reproduced or copied in any form or by any means without the written permission of General Cable.
Characteristic impedance corresponds to the input impedance of a uniform transmission line of infinite length, i.e., Zin = Vi /II It also corresponds to the input impedance of a transmission line of finite length that is terminated in its own characteristic impedance. In general, the characteristic impedance is a complex number with a resistive and reactive component. It is a function of the frequency of the applied signal, and is unrelated to length. At very high frequencies, the characteristic impedance asymptotes to a fixed value which is resistive. For example, coaxial cables have an impedance of 50 or 75 Ohms at high frequencies. Typically, twisted-pair telephone cables have an impedance of 100 Ohms above 1 MHz. Characteristic impedance is of prime importance for good transmission. Maximum power transfer occurs when the source has the same impedance as the load. Thus for sending signals over a line, the transmitting equipment must have the same characteristic impedance as the line to get the maximum signal into the line. At the other end of the line, the receiving equipment must also have the same impedance as the line to be able to get the maximum signal out of the line. Where impedances do not match, some of the signal is reflected back towards the source. In many cases this reflected signal causes problems and is therefore undesirable. The formulae for characteristic impedance are:
Characteristic impedance changes considerably with frequency, particularly from DC to about 100 kHz. Simplified formula may be derived from the one above. At DC ( 0kHz)
At voice frequencies (eg 1kHz)
At high frequencies (> 100 kHz)
For twisted pair and coaxial cables, the resistance is determined by the diameter or weight of copper, the inductance is very small, and the shunt conductance is small. The major influence on characteristic impedance and other secondary coefficients is the capacitance. This is largely determined by the type of insulation (dielectric) used. Characteristic impedance, for high frequencies, can be stated in terms of the physical dimensions of the cable. These formulae apply to copper conductor cables:
For twisted pair:
For coaxial cable:
These formulae show that the characteristic impedance of any cable is directly determined by the conductor sizes, the spacing between them and the type of insulation used. Any change in these will affect the characteristic impedance.
General Cable New Zealand HEAD OFFICE 75-89 Main South Rd PO Box 8044 Riccarton Christchurch Ph: (03) 348 5199 Fax: (03) 348 2009 Website: www. generalcable.co.nz
General Cable Australia Pty Ltd Sales: 1300 363 282 Fax: 1300 363 382 www.generalcable.com.au
Diagrams of cables are illustrative only and are not necessarily to scale. This brochure is distributed with the understanding that the authors and editors are not responsible for the results of any actions taken on the basis of information in this work , or any errors or omissions. Further, General Cable is not engaged in rendering professional services. General Cable expressly disclaims all and any liability to any person in respect of anything and of the consequences of anything done or omitted to be done by any such person in reliance whether whole or partial of the whole or any of the contents of this publication. All rights reserved. No part of this work covered by copyright may be reproduced or copied in any form or by any means without the written permission of General Cable.
