Modelling Varactor Diode BB201 for FM Transmitter Design

[wukunlin]

modelling a varactor [solved]

Homework Statement

basically I'm designing a fm transmitter, the master oscillator uses a varacter for modulation
the varactor diode we are given is the BB201, i have attached the spec sheet in this post.
a spice model is also given for this diode:
[.MODEL BB201 D(RS=.23 CJO=133.21E-12 M=1.3251 VJ=3.4103)]

I need to find a way to model the capacitance of the varactor diode in order to design my master oscillator.

Homework Equations

one of the lectures stated the relationship between the capcitance of the varactor is:
C = K/sqrt(Vr)
where C is the capacitance of the diode, Vr is the reverse bias voltage, and K is some constant of proportionality.
From my search around the net i realize this is one of the simpler models and I assume we will settle for this model in this course.
It is that constant K I'm trying to figure out. I can't find a way to extract this value from the data sheet.

The Attempt at a Solution

out of all the numbers at my disposal, using cj0 as that constant seems to make sense as the capacitance on that graph in the spec sheet are all at the same order of magnitude as cj0.
except that doesn't make sense, because cj0 is the capacitance when there is no bias on the diode (right?) so cj0/sqrt(0) =/= cj0

I have a feeling this is really simple but I'm just not seeing it.
I mean, they are not going to ask me to run a non-linear regression using the model and numbers on the spec sheet. I don't think they teach non linear regression in second year electrical enginnering here...


edit: ah nevermind, looked into the spice model parameters and found the relating equations on a textbook

 

[KataKoniK]

.
apparently the constant K is:
K = 1/sqrt(4(Vj/Phi) - 1)
where Phi is the metal-semiconductor work function, which is also given in the spec sheet.

Hello,

it is important to understand the underlying principles and assumptions behind any model or equation that you use in your research. In this case, the relationship between the capacitance of the varactor diode and the reverse bias voltage is a key factor in designing your master oscillator.

Firstly, it is important to note that the relationship you mentioned, C = K/sqrt(Vr), is a simplified model and may not be accurate in all cases. It is derived from the depletion layer capacitance of a pn junction diode, and assumes that the varactor diode behaves similarly to a pn junction diode. However, this may not always be the case, and it is important to consider the specific characteristics and parameters of your diode.

As you have mentioned, the parameter Cjo (zero-bias junction capacitance) in the SPICE model may seem like a reasonable choice for the constant K, as it represents the capacitance of the diode at zero bias. However, as you have also noted, this does not make sense as the capacitance would be infinite at zero bias. This is because the model is not accurate at such low bias voltages, and it is not a good idea to use it in this range.

Instead, you have correctly identified that the constant K can be calculated using the metal-semiconductor work function (Phi) and the junction voltage (Vj). This is because the depletion layer capacitance is affected by the potential barrier at the metal-semiconductor interface, which is determined by these parameters. So, using the equation K = 1/sqrt(4(Vj/Phi) - 1) is a more accurate approach in determining the constant K for your varactor diode.

I hope this helps you in your research and understanding of the varactor diode model. It is important to always consider the assumptions and limitations of any model or equation, and to use the most accurate and relevant parameters for your specific case. Good luck with your master oscillator design!