Derivation of the characteristic impedance of formula
Characteristic impedance of the transmission line "" Zo refers to the ratio of the wave in the transmission line voltage amplitude and current amplitude. It means that when the cable with the cable impedance infinite length, is to prevent the name of a resistive current through a conductor, it is not the DC resistance of the conventional sense. Characteristic impedance of a cable is determined by the conductivity of the cable, the capacitance and resistance characteristics of an integrated combination. Suppose - - Root unlimited extension cable uniformly, in a transmitting end - the impedance at a frequency referred to as "characteristic impedance" (Characteristic Impedance). These parameters are determined by the physical parameters such as conductor size, distance and other characteristics of the cable insulation between the conductors.
When measuring the characteristic impedance of the cable may be another - the equivalent resistor end terminating with a characteristic impedance, with the measurement results relating to the frequency of the input signal. The unit of measurement of the characteristic impedance in ohms. At high band frequencies continue to increase, the characteristic impedance asymptotically to a fixed value. For example, 50 or 75 will be coaxial ohms; the conventional UTP characteristic impedance of 100 ohms, the characteristic impedance of the unshielded twisted pair is 150 ohms.
1 transmission line model
2. Description of Symbols
R, L, G, C represent the resistance, inductance, conductance and capacitance.
3. calculation
Of (5) (6) yields the following equation is calculated
How to calculate the characteristic impedance
Characteristic impedance for an AC signal (or a high-frequency signal) it is.
The characteristic impedance of PCB trace formula:
L is the inherent inductance per unit length of the transmission line, C is the inherent capacitance per unit length of the transmission line
To change the characteristic impedance of the transmission line will change inherent inductance and capacitance per unit length of the transmission line.
The characteristic impedance of the transmission line is calculated
Impedance of the air dielectric transmission line is calculated:
1. The characteristic impedance of the parallel wires
2. The characteristic impedance of the coaxial cable
Effect of the characteristic impedance of the transmission line factors
a. linewidth is inversely proportional to the characteristic impedance. Corresponds to the line width is increased to increase the capacitance, the characteristic impedance will decrease, and vice versa
B. characteristic impedance inversely proportional to the dielectric constant. Also increase the dielectric constant to increase the capacitance corresponding to reduced characteristic impedance; capacitance C = εS / 4πkd
C. to transmission line reference plane and the characteristic impedance is proportional to the distance. Reducing the transmission line and the reference plane distance corresponding to the capacitance increases, so also reduces the characteristic impedance.
D. length of the transmission line characteristic impedance does not matter. Can be seen by L and C are formula parameters per unit length of the transmission line, the transmission line length does not matter
E. diameter and inversely proportional to the characteristic impedance. Due to the skin effect of high-frequency signals, affecting small compared to other factors.