Microwave Tech - Analysis of through hole inductance of Circuit Board

For digital circuit board design, the inductance of the through-hole is more important than the capacitance. Each through-hole has a parasitic central inductor. Because of the small solid structure of the through-hole, its characteristics are very pixel lumped circuit elements. The main effect of the through-hole series inductor is to reduce the effectiveness of the power supply bypass capacitor, which will make the filtering effect of the whole power supply worse.

The purpose of the bypass capacitor is to short-circuit the two power planes together at high-frequency board. If an integrated circuit is assumed to be connected between the power supply and the ground plane at point A, there is an ideal surface-mount bypass capacitor at point B. The high-frequency impedance between the VCS and ground plane at the chip weld is expected to be zero.

However, this is not the case. Each connection through-hole inductor that connects the capacitor to the VCC and ground plane introduces a small but measurable inductance. The magnitude of this inductance is approximate:

Where L = through-hole inductance, NH

H = length of through-hole, in

D = through-hole diameter, in

Since the above equation includes a logarithm, a change in the diameter of the through-hole has little effect on the inductance, but a change in the length of the through-hole may cause a large change.

The inductive reactance of through-hole to signal with rising edge velocity of 1ns. First, calculate the inductance:

H =0.063 (through-hole length, in)

D =0.016 (through-hole diameter, in)

T10 ~90%=1.00 (rising edge velocity, ns)

Shunt high-frequency current from the chip. 3.8 Ohms is not low enough. Also keep in mind that the bypass capacitor is usually connected to the ground plane through a hole at one end and also to the + 5V plane through a hole at the other end, so the effect of the inductance through the hole is doubled. The bypass capacitor is mounted on the side of the board closest to the power supply and ground plane to reduce its impact. Finally, any lead between the capacitor and the through-hole will add more inductance. These wires should always be as wide as possible.

Very low impedance can be obtained by using multiple bypass capacitors between the source and ground. For digital products, as a rough guideline, assume that the power supply and ground plane are ideal conductors with zero inductance. We consider only the bypass capacitance and its associated wiring and through-hole inductance. In a particular range, all bypass capacitors will act parallel, reducing the impedance between the power supply and the ground. The effective radius for this effect is equal to 1/12, where 1 is the electrical length of the rising edge. Up to 1/6 of the diameter, all capacitors collectively act as a lumped circuit.

The propagation length of 1ns rising edge in FR-4 material is approximately 1=6in. In this example, a capacitor with a grid spacing greater than 1/12=0.5in would not have any benefit.

For the bypass capacitor of the power supply, the shorter the rise time, the more difficult the bypass becomes. When the rise time is shortened, the effective radius becomes smaller. The number of capacitors in the effective radius decreases with the square of the rise time.

This is a comprehensive problem. As the rise time decreases, the digital turning frequency increases, so that the inductive reactance of each through-hole increases. The result is that for a specific configuration of bypass capacitors operating at a given frequency, the effect is reduced by a factor of eight when we halve the rise time. According to the proportionality criterion, experience gained from one operating high-frequency board range can be easily transferred to a new operating frequency range.