Line impedance is the ratio of complex line voltage to complex line current. You can calculate it with the following equation:
Z(z) = V(z)/I(z).
How do you plot a ZL on a Smith Chart?
By plotting the normalized load impedance on a Smith Chart, the input impedance as a function of line length can be found. To find Z along the line for a particular ZL,
find ZL/Z0 on the chart and draw a circle, centered at
1+j0 through that point.
What is ZL in Smith Chart?
The circle in Figure 3 that runs through zL is known as a
constant VSWR or constant SWR circle
. Since this circle is centered at the center of the Smith Chart, the magnitude of is constant along this curve.
How is Smith Chart calculated?
The Smith Chart allows easy calculation of the transformation of a complex load impedance through an arbitrary length of transmission line. It also allows the calculation of the
admittance Y = 1/Z of an impedance
. The impedance is represented by a normalized impedance z. Once around the circle is a line length of l/2.
What is ZL impedance?
ZL = iωL
. (4) The impedance of an inductor differs from that of a resistor in two ways: it depends on frequency and it is an imaginary number. The dependence of ZL on the frequency arises from the fact that the voltage is propor- tional to the derivative of the current rather than the current itself.
What are the two circles on the Smith chart?
The normalised impedance Smith chart is composed of two families of circles:
circles of constant normalised resistance and circles of constant normalised reactance
.
How do you calculate VSWR?
The VSWR definition states that the VSWR is
equal to the maximum voltage on the line divided by the minimum voltage
. The voltage fluctuations come about as a result of the voltage components from the forward power and the reflected power summing together.
How is load admittance calculated?
In equation [1],
Y_L
is the admittance of the load, which is the inverse of the impedance of the load (Z_L). The real part of Y_L is written as C, and is known as the conductance. The imaginary part of Y_L is written as S, and is known as the susceptance. In equation [3], Y_0 is equal to 1/Z_0.
What is a Smith chart used for?
A Smith chart is developed by
examining the load where the impedance must be matched
. Instead of considering its impedance directly, you express its reflection coefficient Γ
L
, which is used to characterize a load (such as admittance, gain, and transconductance). The Γ
L
is more useful when dealing with RF frequencies.
How do you solve a Smith chart problem?
- Determine the impedance as a spot on the Smith chart.
- Find the reflection coefficient (Γ) for the impedance.
- Having the characteristic impedance and Γ, find the impedance.
- Convert the impedance to admittance.
- Find the equivalent impedance.
What VSWR means?
VSWR (
Voltage Standing Wave Ratio
), is a measure of how efficiently radio-frequency power is transmitted from a power source, through a transmission line, into a load (for example, from a power amplifier through a transmission line, to an antenna). … VSWR measures these voltage variances.
What is Smith chart and its applications?
The Smith Chart is
the graphical representation of a complex mathematical equation
. It is the circular plot of the characteristics of microwave components. The Smith Chart is the most used tool for microwave engineers to visualize complex-valued quantities and calculate the mapping between them.
What happens if impedance is not matched?
If the impedances aren’t matched,
maximum power will not be delivered
. In addition, standing waves will develop along the line. This means the load doesn’t absorb all of the power sent down the line.
What is Normalised impedance?
Normalized impedance means
impedance divided by the characteristic impedance
