Simple transistor problem

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In summary, the conversation discusses a problem where the value of resistance and the channel widths of two transistors need to be found. The current and voltage values are given, but there is confusion about how the voltage is divided between Vgs and Vds. The solution is eventually found by realizing that Vgs and Vds are equal.
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[SOLVED] Simple resistor problem

Edit: Oh bullocks! Just noticed the thread title is: "simple resistor problem" when it's obviously supposed to be transistor. Can't seem to be able to edit the topic, though.

Homework Statement



The problem statement is as follows:
Find the value of the resistance R and the channel width W1 and W2 of the following transistors.
http://img86.imageshack.us/img86/6320/transistornw3.jpg [Broken]
This is what we know: The current Id over the resistor is 120 μA, and the voltage in a is 3.5v, and in b it's 1.5v. The rest of the information is given on the picture.


Homework Equations


Relevant equations for this has to be the equations for current through a resistor in the triode-region and the saturation region, namely;
Id = K'n(W/L)((Vgs-vt)vds - 0.5vds^2))
and
Id = 0.5K'n(W/L)(Vgs-vt)^2


The Attempt at a Solution



Finding the resistance for R was rather easy. Considering there's 3.5 volt in point a, there has to have been a voltage drop of 1.5 volt over the resistance.
1.5volt/(120*10^-6) = 12500 ohms.

The real problem I'm having here is realizing how the voltage splits between Vgs and Vds when they're both from the same voltage supply, if you get my drift. What I can say however is this;
Vgs has to be greater than Vt considering a current is supposed to flow through the resistor, so we can't be in the cut off area.
Also, if transistor b only requires 1.5 volt to sustain the current ID, I guess we can conclude that the width of transistor b is larger than that of transistor a. After this however, I'm stumped.

I can't really use any of the formulas without knowing Vgs or Vds. I can say that Vgs + vds = 2V for the first transistor, but this leaves me with three unknowns (W, vgs and vds) and only two equations, and regardless if this I don't even know what region they're operating in.

If anyone could give me a little pointer to help me understand how voltage is divided in a transistor where both vgs and vds draws voltage from the same supply, it would be greatly appreciated.

Thanks!
 
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  • #2
Doesn't Vgs=Vds?
 
  • #3
Gah, can't believe it was that simple!
Thank you, anyway! I knew I should've tried that. I was tinkering with the idea since a kirchhoffs voltage law on just the "left side" of the circuit revealed that the voltage vds had to be equal to vgs and that there would be respectively 2 volt over each of them for the first transistor and 1.5 on the second!
 

1. What is a simple resistor problem?

A simple resistor problem is a type of circuit analysis problem that involves calculating the voltage, current, or resistance of a circuit that contains only resistors, without any other components such as capacitors or inductors.

2. How do I solve a simple resistor problem?

To solve a simple resistor problem, you will need to use Ohm's Law, which states that voltage (V) is equal to current (I) multiplied by resistance (R). You will also need to use Kirchhoff's Laws, which state that the sum of currents entering a node in a circuit must equal the sum of currents leaving the node, and that the sum of voltage drops in a closed loop must be equal to the sum of voltage rises.

3. What is the unit of measurement for resistance?

The unit of measurement for resistance is the ohm (Ω), which is equivalent to one volt per ampere (V/A). This unit is named after the German physicist Georg Ohm, who first described the relationship between voltage, current, and resistance in 1827.

4. Can resistors be connected in series and parallel?

Yes, resistors can be connected in series and parallel to create more complex circuits. In series, the resistors are connected end-to-end, and the total resistance is equal to the sum of each individual resistance. In parallel, the resistors are connected side-by-side, and the total resistance is calculated using the formula: 1/Rtotal = 1/R1 + 1/R2 + 1/R3 + ...

5. Are there any limitations to using Ohm's Law to solve simple resistor problems?

Yes, Ohm's Law assumes that the resistors in the circuit have a constant resistance and that the circuit is in a steady state. It also does not take into account any non-ohmic behavior of resistors, such as changes in resistance with temperature. Additionally, Ohm's Law may not be applicable for circuits with non-linear elements, such as diodes or transistors.

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