# Question about LRC Circuit and Filter

• chingkui
In summary, this circuit cannot act as a filter anymore if we place any load (at least not as the same filter when Z_CD is not there).

#### chingkui

In the diagram, Z1 and Z2 are the impedence of some combinations of L, R and C. The voltage input is placed across AB, and the output voltage is measured across CD. Z1 and Z2 can be designed to make the circuit a filter for output voltage V_CD. However, if we really place a load across CD, it will have an impedence Z_CD, the whole circuit will be affected and the output behavior V_CD will change. Then, the circuit cannot act as a filter anymore if we place any load (at least not as the same filter when Z_CD is not there). How can we say in the first place that the circuit act as a filter? The "filter" only "works" in the absent of load. How useful is LRC circuit as a filter then?

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The short answer is cicuits are designed with very high Z_in(not always but quite often and for the reason you mentioned) thus when you put Z_2 in parallel with a load of Z_in you end up with:

$$Z_{tot}=\frac{1}{\frac{1}{z_2}+\frac{1}{z_{in}}}$$

so as Z_in appraches infinity it has less and less effect on the filtering capability of Z_1 and Z_2.

Try it. Just pick some numbers for Z_1, Z_2, and Z_in (these can all be real BTW). Choose a small Z_in and reiterate with increasing Z_in's and watch as Z_tot approaches Z_2.

Alternetly, you design your filter for a specific circuit and account of the Z_CKT you are connecting your filter to.

Or, you design your filter for a range of Z_in's.

There are a few ways around the problem you've mentioned you just have to realize that when designing ckts you try to design value for some characteristic X but you do so knowing that every component you use will be off of its rated value by some percentage and interconnecting systems may have unknown Z's. So, real world design is more about dealing with these little problems than simply saying "I want value X exactly and if I can't have then the circuit is a failure."

Hope this helped.

The short answer is cicuits are designed with very high Z_in... so as Z_in appraches infinity it has less and less effect on the filtering capability of Z_1 and Z_2
Wouldn't it significantly limit the power transfer to the output?

## What is an LRC circuit?

An LRC circuit is a type of electrical circuit that consists of an inductor (L), a resistor (R), and a capacitor (C). These components are connected in series or parallel and can be used to filter, amplify, or tune electrical signals.

## What is the purpose of an LRC circuit?

The purpose of an LRC circuit is to filter or shape electrical signals. Inductors and capacitors have the ability to store energy in the form of magnetic and electric fields, respectively. By combining these components with a resistor, an LRC circuit can selectively filter out certain frequencies of an electrical signal while allowing others to pass through.

## How does an LRC circuit differ from other types of circuits?

An LRC circuit differs from other types of circuits, such as RC (resistor-capacitor) or RL (resistor-inductor) circuits, in that it incorporates all three components (resistor, inductor, and capacitor). This allows for more complex filtering and tuning capabilities.

## What is the role of a filter in an LRC circuit?

A filter in an LRC circuit is used to selectively pass certain frequencies of an electrical signal while attenuating others. This is achieved by adjusting the values of the inductor, resistor, and capacitor to create specific frequency responses.

## How do LRC circuits affect the frequency response of a signal?

LRC circuits can affect the frequency response of a signal by altering the amplitude and phase of different frequencies. The values of the components in the circuit determine the cutoff frequency, bandwidth, and resonance frequency, which all impact the frequency response of the signal.