Design Amplifier w/ 1k & 10k Resistors for +10 V/V Gain

In summary, the homework statement discusses a circuit design problem that is caused by the inverting amplifier gain being unrealistically large. The homework states that the problem can be corrected by adding a few extra resistors around ##R_2##. The circuit will realize a gain of 10 with the addition of just four resistors.
  • #1
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Homework Statement



Given the availability of resistors of value 1 kΩ and 10 kΩ only, design a circuit based on the non-inverting configuration to realize a gain of +10 V/V.

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The Attempt at a Solution



So I was doing some of those good old design problems, and I came across this one.

I know the gain of the standard non-inverting configuration is given by ##\frac{v_o}{v_i} = 1 + \frac{R_2}{R_1}##. So I want to design the circuit such that:

$$10 = 1 + \frac{R_2}{R_1} \Rightarrow \frac{R_2}{R_1} = 9$$

I'm limited to only the ##1k## and ##10k## resistors provided, and this provides a design problem. Usually, we would like the input impedance to be a large as possible to retain as much of the signal in accordance with ##V = IR##. Similarly, we would like the output impedance to be as small as possible. Looking at the equation:

$$\frac{R_2}{R_1} = 9$$

It doesn't take long to realize I must choose ##R_1 << R_2##, which of course is the exact opposite of what a good amplifier should have. Ideally I want to choose ##R_1 >> R_2##, but I can't figure out the ideal resistor values.

Is this just a bad amplifier design?
 
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  • #2
If Vin is applied to the + input of the op amp then the input impedance it sees is that of the op amp, i.e. very large indeed. The feedback loop involves the op amp output and the - input of the op amp only.

Don't be afraid to stick several of the available resistors in series to make up larger values, after all it is an academic not an economic exercise :)
 
  • #3
The inverting amplifier suffers from a low input impedance problem in general; it causes a problem because ##R_2## can potentially be unrealistically large (this is easy to see considering the inverting amplifier gain). The problem can be corrected by adding a few extra resistors around ##R_2##; Adding a resistor ##R_3## in parallel with ##R_2## using the virtual ground at the input terminals, and a resistor ##R_4## just before the output node.

The gain is then (which we want to be 10V/V):

$$\frac{v_o}{v_i} = - \frac{R_2}{R_1}\left(1 + \frac{R_4}{R_2} + \frac{R_4}{R_3} \right) = 10 \frac{V}{V}$$

Choosing ##R_1 = 10k##, we would need to choose ##R_2 = 10k## so the first term is unity. This makes it easier to select ##R_4## and ##R_3## so the gain is 10. Choosing ##R_4 = 10k## to preserve the signal, and ##R_3 = 0.833k## to satisfy the equation, the circuit will realize a gain of 10.

Now there's an issue, I can only use ##1k## and ##10k## resistors, so ##R_3## is going to have to be some combination of resistors.

Sticking 5 ##1k## resistors in series, and then putting those in parallel with another ##1k## resistor, provides the desired resistance.
 
  • #4
Zondrina said:
It doesn't take long to realize I must choose ##R_1 << R_2##, which of course is the exact opposite of what a good amplifier should have. Ideally I want to choose ##R_1 >> R_2##, but I can't figure out the ideal resistor values.

Is this just a bad amplifier design?
How about one feedback resistor & one to gnd, then dividing the + input down to get Av = 10?
Total no. of resistors = 4.
 
  • #5


I would first assess the limitations and constraints of the given problem. In this case, we are limited to using only 1kΩ and 10kΩ resistors, which may not be ideal for designing an amplifier with a specific gain. However, given these limitations, we can still design a functional amplifier.

One approach could be to use a combination of resistors in parallel and series to achieve the desired gain of +10 V/V. For example, we could use two 1kΩ resistors in parallel to create an effective resistance of 500Ω, and then use a 10kΩ resistor in series with this to achieve a total resistance of 10.5kΩ. This would result in a gain of 10.5 V/V, which is close to the desired gain of +10 V/V.

Another approach could be to use a combination of resistors in a voltage divider configuration. For instance, we could use a 1kΩ resistor as the input resistor and a 10kΩ resistor as the feedback resistor, resulting in a gain of 10 V/V. However, this would also decrease the input impedance of the amplifier, which may not be desirable.

In conclusion, while the given constraints may not allow for an ideal amplifier design, it is still possible to design a functional amplifier with a gain of +10 V/V using the available resistors. It may require some creativity and trade-offs, but it is a good exercise in problem-solving and utilizing the resources at hand.
 

1. What is a design amplifier?

A design amplifier is a type of electronic circuit used to amplify a signal. It is typically composed of resistors, capacitors, and transistors, and is designed to increase the strength of a signal without distorting it.

2. What is the purpose of using 1k and 10k resistors in a design amplifier?

The 1k and 10k resistors are used to set the gain of the amplifier. By using these specific resistor values, the amplifier will have a gain of +10 V/V, meaning the output voltage will be 10 times greater than the input voltage.

3. What does a gain of +10 V/V mean?

A gain of +10 V/V means that for every 1 volt of input, the output voltage will be amplified by a factor of 10. For example, if the input voltage is 0.5 volts, the output voltage will be 5 volts (0.5 x 10 = 5).

4. How does a design amplifier with 1k and 10k resistors work?

The 1k and 10k resistors are arranged in a specific configuration, called an inverting amplifier, which uses negative feedback to amplify the input signal. The 1k resistor is connected between the input and the inverting input of the amplifier, and the 10k resistor is connected between the inverting input and the output. This configuration allows for precise control of the gain of the amplifier.

5. Can the gain of the amplifier be adjusted?

Yes, the gain of the amplifier can be adjusted by changing the values of the resistors. For a higher gain, the value of the 10k resistor can be decreased, and for a lower gain, the value can be increased. However, it is important to keep in mind that changing the resistor values can also affect other properties of the amplifier, such as its bandwidth and stability.

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