CHARACTERISTIC IMPEDANCE

The characteristic that is most important characteristic of any transmission line is its characteristic impedance, Z0. CI(characteristic Impedance) is defined as the ratio between the voltage and current

Characteristic Impedance Ratio = (v/i),

at the input of a line of infinite length. If the impedance value of the signal source is equal to Z0, all of the power that is generated by the source is transferred to the line. Opposing to this, if there is an impedance level Z0 at the far end point of the line, all the power of the signal shall be transferred to this. It implies that a lossless line transfers all the power from a source to the receiver.

But, to make it happen, the source and receiver impedances must be at equal level (matched) to the line impedance. If the impedance level at the far end of line is not equal to Z₀ (including event when it is an open circuit, or when there is a short circuit) part of or all of the energy of the signal is reflected back along the line. This makes the standing waves to form in the conductors, and only very few power is transferred to the receiver. For having quick transmission of signals, this should be avoided by careful matching of impedances.

The level of characteristic impedance of a cable at high frequencies largely depends on the value of inductance and capacitance per unit length of cable. characteristic impedance is independent of frequency level, only when the frequency is high. Or say in other words, the piece of cable behaves like a pure resistance, which remains fixed, regardless of the frequency.

In real practices, all the cables are made with standard characteristic impedances. Transmission hardware has input or output impedances the value of which matches with these standards. The easily available value of Z0 for coaxial cable is 50 Ω, the another common value is around 75 Ω. The twisted pairs have standard impedances ranges between the 300 Ω to 600 Ω. With lower frequency levels, the impedance varies with the level of frequency. There is a particular range of frequencies that the line can transmit without any significant loss of power is called bandwidth of the line. The bandwidth level ranges from the lowest frequency to the highest frequency levels and at that point the output signal is less than 3 dB below the input signal.

The graph presented below shows us the simulation of a transmission line that consists of a twisted pair of copper wires having characteristic impedance of 600 Ω and the length is 200 m.

In the above chart the amplitude of the signal that is across the load at the receiving end is plotted against frequency. Both are plotted on logarithmic scales, Decibels scale is used for plotting amplitude. The line that is at 23 dB shows us the half-power level. Signal strength rises up above half power at 25 Hz and falls below it at 3 kHz. We can define the bandwidth of this system as the difference between these two frequencies, which comes out to be 2972 Hz.