What is the Relationship Between Resistor Values in an Attenuator Circuit?

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In summary, the problem is to find the values of R1 and R2. I have tried manipulating the known answers to find the correct algorithm(big word that) but cannot find the correct method. I suspect it turns into some kind of quadratic but its been so long ago since I played with this stuff.
  • #1
profbuxton
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Homework Statement
Find R1 and R2
Relevant Equations
(R1+R2 +Ro) /R2 = 5 where Ro = SQRT(R1 x R2+(R1 x R1) / 4) = 60
Greetings, fellow travelers.
I gave been digging into some of my old (1970s) Electronic maths textbooks and for my amusement and time wasting refreshing some old knowledge. Have got through a fair but but have to keep coming back to this problem.
I do have the answers but I cannot regardless of how I manipulate the variables I can't seem to find the correct method obtain the answer. This problem is in part of the book related to solving quadratics but I can't see how this is related. Any broad hints at a solution would help me sleep better. Thanks for your assistance.

PS sorry about the format of the equations. Havent used the system to enter equations before. Maybe I will learn that too!
 
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  • #2
Greetings too.
What's the complete problem statement ? Any diagrams ?
 
  • #3
sorry no diagrams with this problem.
The problem is to find the values of R1 and R2. I have tried manipulating the known answers to find the correct algorithm(big word that) but cannot find the correct method. I suspect it turns into some kind of quadratic but its been so long ago since I played with this stuff.
 
  • #4
EDIT. Sorry - didn't spot that the value of R₀ is given. The reply (below) is therefore not relevant. See Post #6 instead.

There are three unknowns (R₀, R₁ and R₂) but only two equations. So you can’t solve for the values of R₁ and R₂.

Maybe you are meant to express R₁ and R₂ in terms of R₀. For example:
R₁ = 2.5 R₀ and R₂ = 0.2R₀
(not the answers, just some random made-up numbers for illustration).

If this is the case let R₁ = aR₀ and R₂ = bR₀. The problem is then to find a and b.

Substitute for R₁ (replace it by aR₀) and for R₂ (replace it by bR₀) in your equations.
You will get two equations containing only a and b. See if you can solve these.
 
Last edited:
  • #5
Oh, sorry for the misunderstanding. The value for Ro is given by the equation
Ro = SQRT(R1 x R2+(R1 x R1) / 4) = 60 so in the first eqn. Ro actually equals 60.
sorry if it wasnt too clear . my bad. does that help?
 
  • #6
profbuxton said:
Oh, sorry for the misunderstanding. The value for Ro is given by the equation
Ro = SQRT(R1 x R2+(R1 x R1) / 4) = 60 so in the first eqn. Ro actually equals 60.
sorry if it wasnt too clear . my bad. does that help?
Whoops – my mistake. Sorry. See if this gets you started...

Replace R₀ by 60 and you get two equations:
(R₁+ R₂ + 60) / R₂ = 5 (equation 1)
√(R₁R₂ + R₁²/4) = 60 (equation 2)

Rearrange equation 1 to make R₁ the subject.
Square both sides of equation 2 to get a new equation without the square root.
Can you take it from there?

If you need a reminder on how to solve quadratic equations, see here for example: https://www.bbc.co.uk/bitesize/guides/zwmyxfr/revision/1
 
  • #7
profbuxton said:
Oh, sorry for the misunderstanding. The value for Ro is given by the equation
Ro = SQRT(R1 x R2+(R1 x R1) / 4) = 60 so in the first eqn. Ro actually equals 60.
sorry if it wasnt too clear . my bad. does that help?

In LaTeX:
$$R_0 = \sqrt{R_1 R_2 + \frac{R_1^2}{4}}$$

See the LaTeX Guide link below the Edit window. :smile:
 

Related to What is the Relationship Between Resistor Values in an Attenuator Circuit?

1. What is an attenuator resistor?

An attenuator resistor is a type of electronic component that is used to reduce the strength of an electrical signal passing through a circuit. It is often used in audio and radio frequency circuits to control the volume or intensity of a signal.

2. How do attenuator resistors work?

Attenuator resistors work by creating a voltage divider in a circuit. This means that they divide the incoming voltage into smaller parts, reducing the overall strength of the signal. The amount of attenuation is determined by the ratio of the resistor values in the circuit.

3. What are the different types of attenuator resistors?

There are two main types of attenuator resistors: fixed and variable. Fixed attenuator resistors have a set value and cannot be changed, while variable attenuator resistors allow for adjustment of the attenuation level. Variable attenuator resistors are often used in audio equipment to control volume levels.

4. How do I choose the right attenuator resistor value?

The value of an attenuator resistor depends on the specific circuit and the amount of attenuation needed. It is important to consider the input and output impedance of the circuit, as well as the desired level of attenuation. Generally, the higher the resistor value, the greater the attenuation.

5. Can attenuator resistors be used in any type of circuit?

Attenuator resistors can be used in a wide range of circuits, including audio, radio frequency, and power circuits. However, it is important to select the appropriate type and value of resistor for the specific circuit to ensure proper functioning and avoid potential damage to the components.

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