Transmission Line Properties
We will now explore several properties of the Transmission Line. We will explore inductance and capacitance per unit length, propagation delay and characteristic impedance and their relation to the properties of the transmission line.
9.3 Capacitance and Inductance Per Unit length of the Transmission Lines
Each uniform transmission line has a finite capacitance per unit length and finite inductance per unit length. The capacitance per unit length and finite inductance per unit length depend upon the physical dimensions of the components of the transmission line (e.g. the trace width and trace to ground layer separation in PCB trace transmission line).
The ratio of these two parameters must have a fixed value throughout the length of the transmission line to achieve distortion less propagation of the signal.
As an example take a look at 10 inches of the microstrip transmission line. As shown in the figure below.
Figure 9.1 A 10 inch long microstrip transmission line
Leave the other end of the transmission line open and measure the capacitance on the one end of the transmission line. If the trace width of the transmission line is 5 mils ( 0.005”) and its separation from the ground layer is 5 mils ( 0.005”) then this should give a capacitance of the order of 20 pf assuming the relative permittivity of the material between transmission line and ground to be 4.0.
Figure 9.2 – Inductance of a Transmission Line
Now mentally short the traces on the other end of the transmission line and measure the inductance on the one end of the transmission line. This should give an inductance of 10 nH. This corresponds to 1.0 nH per inches.
In the next two sections we will see how the capacitance per unit length and the inductance per unit length determine the propagation delay and the characteristic impedance of the transmission line.
9.4 Propagation Delay
The electric signal takes finite amount of time in propagating from one point to another along the transmission line. The propagation delay is defined as the amount of delay per unit length of the transmission line. In metric the unit of propagation delay is seconds/meter or more conveniently, ns/meter. The velocity of light in vacuum is 3x108 meter/second. This corresponds to propagation delay of 3.33x10-9 seconds /meter or 3.33 ns /meter.
A more convenient unit for propagation delay for PCB designers is picoseconds per inches. The propagation delay corresponding to the speed of light in vacuum is 84.7 ps/inch. The electric signals in PCB traces travel at a smaller speed. The speed is typically about 50% of the free space speed. The typical propagation speed is 150 ps/inches.
The propagation delay can be defined as a function of the capacitance per Unit length and inductance per unit length as follows
Tpd = √(LC) ------------[9.2]
where,
Tpd = Propagation delay in seconds/inch
L= inductance per unit length H/inch
C= capacitance per unit length F/inch
The above equation computes the propagation delay in second/inches. This unit is convenient for PCB designers.
Previous - Transmission Line Next - Transmission Line Characteristic Impedance