Varactor Diodes–What Are They And How Are They Useful?
Varactor diodes are used in applications which require a variable capacitor. A varactor is a voltage dependent capacitance which can be used to tune a Voltage Controlled Oscillator (VCO) or the phase of a phase shifter. An important step in creating a product that uses a varactor diode is development of an accurate model of the device. This article outlines a step by step procedure to develop a varactor diode model. It is assumed that the circuit using the varactor has a rf power level that can be considered small signal. In other words, it is assumed that the rf signal is low enough that it does not create significant non-linear effects in diode.
Varactor Diode Model
Before the first step can begin, it is important that the basic model of the varactor diode is discussed. Figure 1 shows the symbol for a varactor diode and its equivalent electrical model at high frequencies. The package inductance, Lp, is due to the lead inductance, wirebonds and other interconnect required to get to the diode device. The package capacitance, Cp, is due to the stray capacitance from the package and other features to the surrounding ground. In general, better quality diodes have minimal package effects and therefore Cp and Lp are small. In fact, for bare die devices, Lp and Cp can be minimized.
The device resistance, R(V) is the device resistance in the physical diode and will have some voltage dependence. For some applications with a limit tuning voltage range, the voltage dependence of the resistance can be ignored. The resistance accounts for the finite Q of the diode and is due to the undepleted region of the diode and contact resistance. The tuning capacitance, C(V), is the desired capacitance and it is strongly dependent upon the bias voltage.
The goal of this article is to present a procedure to find the values of the diode model so that it can be used in the design of a circuit.
Figure 1. The schematic symbol and electrical model of the varactor diode.
Step 1: Determine capacitance tuning curve
The first step is to generate the diode capacitance equation to model C(V). The diode manufacturer will supply table of varactor capacitance versus bias voltage. If the manufacturer of the diode you are considering does not publish this or will not supply it to you when asked, then choose a different diode manufacturer. Since the model will be used in a circuit simulator, the goal is to generate an equation which will accurate predict C(V) over the expected range of V.
The equation used to model the capacitance is:
C(V) = Varactor diode capacitance
Co = Zero bias capacitance
V = Reverse bias voltage
Φ = Built-in potential
γ= slope of the LogC vs. LogV curve
For our example, we are using a Skyworks SMV1413 diode. The manufacturer’s datasheet contains a table of the device capacitance versus reverse bias voltage. Table 1 shows the capacitance table from the fabricator C(pF) and the predicted capacitance, curve fit, using Equation 1. For the table it can be seen that the maximum error in the curve fit equation is about 1/2 of one percent.
Table 1. Capacitance tuning table using Co=9.24pF, Φ=0.78 and γ=0.45.
Step 2: Determine Diode Resistance
The determination of the diode resistance can be quite complicated. A very rigorous method involves electrical measurements on diode samples as a function of reverse bias voltage and frequency. The resistance can be determined from the variation of Q.
A simple method is to use the manufacturers measured Q. From the datasheet it can be seen that the Q is 2400 at a bias of 4V at 50MHz. From this information and from Equation 2 below it is possible calculate the series resistance as 0.33 ohms
Rs = diode resistance
ω = 2πf
f = frequency
Cj = diode capacitance
Step 3 Include Package Inductance and Capacitance
The diode package inductance and capacitance can be determined using measured data. However, for many diodes these parameters are included in the datasheet. For our diode, the manufacturer specifies Cp as 0.3 pF and Ls as 0.55 nH.
The development of a diode model is simplified if the manufacturer supplies some of the parameters. This article presented a method to convert the manufacturer datasheet into a useable device model capable of being used in a product design. This method has been used to develop models for phase shifters, VCOs and VXO products.