Calculation of characteristic impedance
Simple characteristic impedance model: Z=V/I, Z represents the impedance at each step in the signal transmission process, V represents the voltage when the signal enters the transmission line, and I represents the current.
I=±Q/± T, Q represents the quantity of electricity, and T represents the time of each step.
Power (from the battery) : ±Q=±C×V, C represents the capacitance, V represents the voltage.
Capacitance can be derived from the capacity CL per unit length of the transmission line and the signal speed v.
The length of unit pin is taken as the velocity, and then multiplied by the time required for each step, t, to obtain the formula: ±C= Cl × V ×(±)t.
Comprehensive above, we may safely draw the characteristic impedance, Z = V/I = V/(+ Q / + t) = V/(x + C V / + t) = V/(CL * V/V * (+) t + t) = 1 / (CL (V)
It can be seen that the characteristic impedance is related to the capacity per unit length of the transmission line and the signal transmission speed.
In order to distinguish the characteristic impedance from the actual impedance Z, we add 0 after Z. The characteristic impedance of the transmission line is: Z0=1/(CL× V)
If the capacity per unit length of the transmission line and the signal transmission speed remain constant, then the characteristic impedance of the transmission line also remains constant.
This simple explanation connects the common sense of capacitance with the newly discovered theory of characteristic impedance.
If the capacity per unit length of the transmission line is increased, such as the thickening of the transmission line, the characteristic impedance of the transmission line can be reduced.
Measurement of characteristic impedance
When the battery is connected to the transmission line (suppose the impedance is 50 ohm at the time), how do you measure the infinite impedance by connecting the ohmmeter to the 3-foot RG58 cable?
The impedance of any transmission line is time-dependent.
If you measure the impedance of a cable in less time than its reflection, you measure the “surge” impedance or characteristic impedance.
But if you wait long enough until the energy is reflected back and received, a change in impedance can be detected by a measurement.
In general, the impedance value will bounce up and down to a stable limit.
For a 3inch ft cable, impedance measurements must be made within 3 nanoseconds. The TDR(Time Domain Reflectometer) can do this by measuring the dynamic impedance of the transmission line. If the impedance of a three-foot cable is measured in one second, the signal will bounce back and forth millions of times, resulting in different “surge” impedances.
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