Saturday, August 3, 2013

Voltage-Controlled Filter Design Theory

Heya folks. I'm currently in the lab at school testing out a simple voltage-controlled filter. I'll show you that in another post soon. But first, I want to share my thought process thus far. I sat down the other night and began writing everything I knew about designing a voltage-controlled filter so I knew what blanks needed to be filled. That writing is below.

Simple RC Filter:



This circuit attenuates particular frequencies (in this case, low frequencies) depending on the value of the components. With a variable capacitor or resistor, the specific frequencies can be attenuated or swept through. A simple mechanical device, called a potentiometer is a variable resistor that can be used in this way. The tone knobs on the front of any typical guitar amp utilize this phenomena.

If the Thevenin resistance and total capacitance of the filter are known, then the corner/cutoff frequency of the filter can be mathematically calculated with the following equation:

F_c = 1/(2*pi*R*C)

For low and high pass filters, the cutoff frequency is the frequency at which the output magnitude equals 0.707 times the input magnitude. Or in layman's turn, the frequency where the filter starts working.

So, with this filter theory behind us, let's talk about designing a voltage-controlled filter. We need some device to replace a potentiometer. So it needs to be a three-pronged device where one input controls the flow of current between two of the other inputs. Well this sounds eerily like our good friend the Field-Effect Transistor!

An FET is an electrical device made of semi-conducting material (commonly silicon). The voltage between the gate and source (V_gs) controls the current flow through the source and drain (I_ds), well not entirely. An FET can operate in two different regions. In the saturation region, the drain current is nearly independent of the drain/source voltage. In the ohmic region, the drain current does depend on the drain/source voltage.

My understanding as of now is that small changes in V_gs result in different resistances between the drain and source, however, you've got to be careful to stay operating in the ohmic region, that depends on what V_ds is. Man this is confusing. The circuit I'm testing now seems to be working this way. I just arbitrarily chose some resistors and a capacitor. I need to sit down and derive a circuit with specific characteristics, then test it in the lab. I was just getting familiar with the topology in the lab today.

Here are the documents I have been studying today. Most of what I've discussed has come from them.

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/filcap.html (Basic high pass filter theory)

http://users.ece.gatech.edu/~lanterma/sdiy/datasheets/transistors/vishay_fet_cvr_an.pdf (The circuit I'm testing today is a modification of Figure 7 in this publication)

http://graffiti.virgin.net/ljmayes.mal/comp/vcr.htm (This discusses making an FET operate linearly in the ohmic region)

Well, I've got o quit for today. More again Monday.
-Mark






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