PCB News - PCB characteristic impedance calculation

The value of the instantaneous impedance seen by the signal during transmission. The impedance Z seen by the signal in each propagation interval is consistent with the basic definition of impedance

Z=V/I
The voltage V refers to the signal voltage added to the transmission line, and the current I refers to the total amount of charge δQ obtained from the battery in each time interval δt, so
I=δQ/δt
The charge flowing into the transmission line (the charge ultimately comes from the signal source) is used to charge the capacitance δC formed between the newly added signal line and the return path in the signal propagation process to the voltage V, so
δQ=VδC
The capacitance caused by the signal traveling a certain distance during the propagation process is related to the capacitance value CL per unit length of the transmission line and the speed U of the signal propagating on the transmission line. At the same time, the distance the signal travels is the speed U multiplied by the time interval δt. so
δC = CL U δt
Combining all the above equations, the instantaneous impedance can be derived as:
Z=V/I=V/(δQ/δt)=V/(VδC/δt)=V/(V CL U δt /δt)=1/(CL U)
It can be seen that the instantaneous impedance is related to the capacitance value per unit transmission line length and the speed of signal transmission. This can also be artificially defined as the characteristic impedance of the transmission line. In order to distinguish the characteristic impedance from the actual impedance Z, a subscript 0 is specially added to the characteristic impedance. The characteristic impedance of the signal transmission line has been obtained from the above derivation:
Z0 = 1/(CL U)
If the capacitance value per unit length of the transmission line and the speed at which the signal propagates on the transmission line remain constant, then the transmission line has a constant characteristic impedance within its length. Such a transmission line is called a controlled impedance transmission line.
It can be seen from the above brief description that some intuitive knowledge about capacitance can be linked with the newly discovered intuitive knowledge of characteristic impedance. In other words, if the signal wiring in the PCB board is widened, the capacitance value per unit length of the transmission line will increase, and the characteristic impedance of the transmission line can be reduced.

The above is the introduction to the calculation of PCB characteristic impedance. Ipcb is also provided to PCB manufacturers and PCB manufacturing technology