# Find Voltage Gain: Deriving Vgs=Vds - Small Signal Circuit

• killerdevil
In summary, the conversation is about the derivation of the equation Vgs = Vds. The speaker is confused about when to look at the original circuit, when to look at the AC circuit, and when to remove the load. The other person explains that the equation makes sense because the current flows from drain to source across the drain resistor, and the voltage at the gate is equal to the voltage at the drain due to the electrical connection between them.
killerdevil

can someone please tell me how did they derive with the above equation?

my point of view:
Vgs = Vin
Vds = Vout

so how did they even get Vgs = Vds?

below shows the Small signal circuit:

might be a stupid question to ask. but i am really confuse on when to look at the original circuit, when to look at the AC circuit, when do i remove the load, etc.

Thanks for helping and sorry for asking such a simple question here.

Last edited:
They're using capital letters, so I don't think they're talking about the small signal values, but rather the DC bias values. It's been a while since I've looked at MOSFETS in detail, but assuming that the transistor is biased in such a way that it will conduct, then

VDS = VDD - IDRD

makes perfect sense, because current flows from drain to source across the drain resistor, so the voltage at the drain will be the supply voltage minus the voltage drop across the drain resistor.

The voltage at the gate is equal to the voltage at the drain, because the two are electrically connected by RG. Since no current flows across RG, there is no potential difference across it. So, it's as though the two terminals are connected by a wire.

As far as I can tell, it's as simple as that.

## 1. How do you calculate the voltage gain in a small signal circuit?

The voltage gain in a small signal circuit can be calculated by taking the difference between the input voltage (Vds) and the output voltage (Vgs), and dividing it by the input voltage. This can be represented by the equation: Vgs/Vds.

## 2. What is Vgs and Vds in a small signal circuit?

Vgs and Vds are two important voltages in a small signal circuit. Vgs refers to the voltage between the gate and the source of the transistor, while Vds refers to the voltage between the drain and the source of the transistor.

## 3. What is the significance of voltage gain in a small signal circuit?

Voltage gain is an important parameter in a small signal circuit as it determines the amplification of the input signal. A higher voltage gain means a larger output signal compared to the input signal, which is crucial for many electronic devices.

## 4. What factors affect the voltage gain in a small signal circuit?

The voltage gain in a small signal circuit can be affected by various factors such as the type of transistor used, the biasing voltage, the load resistance, and the frequency of the input signal. These factors should be carefully considered when designing a small signal circuit to achieve the desired voltage gain.

## 5. How can I improve the voltage gain in a small signal circuit?

To improve the voltage gain in a small signal circuit, you can use a transistor with a higher gain value, adjust the biasing voltage, decrease the load resistance, or use a higher frequency input signal. However, it is important to note that these changes may also affect other parameters of the circuit, so careful analysis and testing is necessary.

• Engineering and Comp Sci Homework Help
Replies
13
Views
2K
• Electrical Engineering
Replies
3
Views
3K
• Engineering and Comp Sci Homework Help
Replies
2
Views
2K
• Engineering and Comp Sci Homework Help
Replies
3
Views
1K
• Engineering and Comp Sci Homework Help
Replies
5
Views
4K
• Engineering and Comp Sci Homework Help
Replies
1
Views
2K
• Engineering and Comp Sci Homework Help
Replies
4
Views
2K
• Engineering and Comp Sci Homework Help
Replies
7
Views
1K
• Engineering and Comp Sci Homework Help
Replies
1
Views
2K
• Engineering and Comp Sci Homework Help
Replies
9
Views
4K