Using SPICE simulation tools to predict impedance.
How many capacitors do you need in the power distribution? When do you need to worry about parallel resonances? What roles do power and ground planes play in the impedance of power delivery network (PDN)? These sorts of questions can be answered with a free software tool that can be run on your desktop.
While the impedance of any interconnect element can be measured with an impedance analyzer and even a network analyzer, it can be simulated using a software tool called SPICE. With a SPICE simulator tool, you can build any circuit model and simulate its impedance, displaying the impedance profile of a combination of capacitors.
Impedance is one of those electrical properties that is used in either the time or frequency domain, depending on the application. For the power delivery network, the frequency domain is most useful.
The heart of a frequency domain impedance analyzer in SPICE is a constant current AC source. No matter what the load is across the terminals of the constant current AC source, an output voltage will be generated so that the current is a sine wave.
By definition, the impedance of a device, Z(f), is the ratio of the voltage across the device to the current through it: Z(f) = V(f)/I(f). If the current is set to exactly 1 A, then the voltage across the circuit we attach is exactly equal to the impedance of the circuit. Figure 1 shows the circuit model to simulate a real capacitor, composed of an RLC circuit.
FIGURE 1. Top: SPICE simulation circuit to simulate the impedance of the RLC circuit. Bottom: Simulated impedance (blue) and measured impedance (red) of the 0603 capacitor, inset.
|
The only elements that can be simulated are ideal elements. The ideal R, L and C components are connected in series and the simulated voltage across the circuit is displayed. This simple model is remarkably close to the actual behavior of a real capacitor component.
When the agreement is this good, it gives us confidence we have an accurate model for the real capacitor component. In this example, we see excellent agreement between the measured impedance (in red) and the simulated impedance of the model (in blue), when we use a value of the equivalent series resistance (ESR) of 0.02 ohms, an equivalent series inductance (ESL) of 1.25 nH and a capacitance of 190 nF.
When building the power delivery impedance profile from a combination of capacitors, an important feature is the parallel resonance, which develops between two real capacitors connected in parallel. With a model for each real capacitor, composed of two RLC series circuits, the parallel resonance can be simulated, as shown in Figure 2.
FIGURE 2. SPICE simulated impedance of two RLC circuits in parallel, showing the high impedance at the parallel resonant frequency.
|
The parallel resonant frequency is when the impedance of the right hand capacitor matches the impedance of the left hand capacitor. At this frequency, the impedance of the combination of capacitors will be a peak. By changing the values of the different R, L and C elements you can explore design space to see how to optimize the capacitor selection to minimize the parallel resonant peak impedance.
SPICE is an incredibly valuable tool to predict the impedance of the combination of capacitors used to construct the PDN. By simulating the impedance of all the capacitors in the frequency domain, the impedance of the PDN can be sculpted to fit your specific needs. PCD&M
Dr. Eric Bogatin is president of Bogatin Enterprises. Many of his papers are available on his Web site, www.BeTheSignal.com. He can be reached at This email address is being protected from spambots. You need JavaScript enabled to view it..
