4.4 The Four-Terminal Capacitor or DTL

The most effective way to provide fast decoupling is to build the capacitor as a four-terminal transmission line. Energy is supplied from one end and taken from the other. In effect, this is a transmission line positioned between a load and a source of energy. We can call this a decoupling transmission line or DTL. The source impedance of this DTL determines the voltage drop when a demand is made for current. The length of the DTL determines how long this voltage is sustained. After a demand for current, the voltage drop depends on the ratio of characteristic impedances. A small wave makes a round trip in the DTL. When the wave returns to the load, the voltage will drop a second time. A loaded four-terminal capacitor is shown in Figure 4.3.

Figure 4.3 A four-terminal capacitor (DTL) in a circuit. The values shown are characteristic impedances.

A practical DTL could have a source impedance as low as 0.1 ohm. A 1-A demand at the load end would cause a voltage drop of 0.1 V. When the resulting wave reaches the far end of the DTL, a wave is both reflected and transmitted depending on the parameters at the discontinuity. If the far end is a short transmission line connected to a voltage source then many round trips can take place in this short line before a second wave makes a round trip in the DTL. Section 2.15 discussed the flow of energy between mismatched transmission lines. The balance of energy flow is given by Equation 2.17. If this condition is met, there will be very little sag in the voltage supplied by the DTL.

The capacitance of a DTL can be expressed in terms of its characteristic impedance and the time it takes for a wave to travel the length of the DTL. If the characteristic impedance is Z and the travel time is t then the capacitance is given by

4.1

As an example, if Z = 0.2 ohm and t = 1000 ps, the value of C is 5000 pF. If the voltage is 5 V and the load is 5 ohm, the voltage will drop to 4.8 V and remain constant for 2t or 2000 ps. Because this voltage is constant, it is correct to say that the source has no series inductance. In practice, any load that is connected to a DTL is another transmission line.

It is interesting to consider the power distribution structure on a circuit board as a network of transmission lines. Every decoupling capacitor that is placed between power and ground is in effect with two-transmission lines in series. The first transmission line is the capacitor and its dielectric that stores a charge and the second line is the connection to the capacitor. These two transmission lines are in effect two-short stubs in series.

When a DTL is placed between a power source and a load, it can provide a 0.1-ohm link. In effect, it looks like a power filter. The DTL reflects voltage fluctuations that arrive from either direction. This, in effect, splits the power structure into two sections. If a DTL is placed next to a noisy source, only a small fraction of the noise will propagate to the other side of the DTL. For this reason, the DTL is a powerful tool in controlling both conducted and radiated interference. It provides decoupling in the full sense of the word.