Analyzing Different Wave forms
When an AC signal is transmitted transmission line some of the signal is reflected back to ward the source this reflected wave come back towards the source but the source cannot observe it due to which it stays in the transmission line which attinuates the transfor of power from source to load becouse it is out of phase w.r.t source.
As shown in the above given diagram of waveform no (a) that the wave of voltage or current which travels from source to load is called the incident wave.
If the load impedance is equal to the characteristic impedance (Zo) then all the energy provided to the load with the help of incident wave will be observed by the load.
If the impedance of the load is not equal to the characteristics impedance, then there will be the miss matching and some of the energy will be reflected back. This reflected wave of voltage and current is shown as wave form no (b).
The resultant waveform which is produced along the transmission line due to interaction of incident wave and reflected wave is known as standing wave. It is shown in the given diagram no c.
Standing Wave Ratio (SWR)
As we know that the standing wave are the resultant of incident wave and reflected wave, therefore, it is also an alternating waveform along the transmission line. When propagation takes place there will be maximum and minimum amplitude of voltage or current. The ratio between the maximum amplitude of voltage or current and the minimum amplitude of voltage or current is known as standing wave ratio. It is abbreviated as SWR.
The ratio between the load impedance (ZL) and the characteristics impedance (Zo) is also called Standing wave ratio.
SWR = (Max V or I) / (Min Vor I)
SWR = ZL/ Zo If ZL > Zo
SWR = Zo / ZL if Zo > ZL
The SWR will always be one or more than one. It will never be less than one.
Voltage Standing Wave Ratio (VSWR)
It is the ratio between maximum voltage and minimum voltage along the transmission line.
VSWR = Max V/ Min V
Current Standing Wave Ratio (ISWR)
It is the ratio between maximum current and minimum current along the transmission line.
ISWR = Max I / Min I
Reflection coefficient is the ratio of voltage and current between the incident wave and reflected wave along the transmission line. It is denoted by Greek latter ϱ Rho.
Voltage Reflection Coefficient
ϱv = Vr / Vi
Where Vr stands for voltage reflected wave and Vi stands for voltage incident wave.
ϱv= (ZL – Zo) / (ZL + Zo)
ZL = Load Impedance
Zo = Characteristic Impedance
Voltage Reflection Coefficient
Voltage reflection coefficient is the ratio of voltage between incident and reflected wave along the transmission line. It is denoted as ϱv.
Current Reflection Coefficient
It is the ratio of current between incident wave and reflected wave along the transmission line. It is denoted as ϱI.
ϱI = Ir / Ii
Need for making (ZL = Zo)
There are the following reasons for which the load impedance is required to be matched with characteristics impedance of the transmission line.
- If the load impedance is equal to characteristics impedance, the maximum power transfer takes place from source to load.
- There is no reflected energy from load towards the source.
- The phase of voltage and current will be the same along the transmission line.