An analysis of the filters implemented with resistors and capacitors

Morehead State University ABSTRACT This paper will explain the basic concepts underlying the operation of the switched capacitor, as well as the use of switched-capacitors to realize compact and versatile circuits already familiar to the undergraduate student of electronics. One set of example circuits include easily tunable active filters; specific examples of filter designs that incorporate switched-capacitors will be developed, and the use of a commercially available switched-capacitor integrated circuit, the MF10, to implement the designs will be shown. Another example circuit is an instrumentation amplifier that is more compact and has a higher CMRR than the conventional realization. Linear Technology's LTC serves as the vehicle for this circuit.

An analysis of the filters implemented with resistors and capacitors

Frequency Response and Active Filters This document is an introduction to frequency response, and an introduction to active filters filters using active amplifiers, like op amps. Frequency Response -- Background Up to now we have looked at the time-domain response of circuits.

However it is often useful to look at the response of circuits in the frequency domain. In other words, you want to look at how circuits behave in response to sinusoidal inputs.

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This is important and useful for several reasons: Therefore if there is an easy way to analyze circuits with sinusoidal inputs, the results can be generalized to study the response to any input. To determine the response of a circuit to a sinusoidal signal as a function of frequency it is possible to generalize the concept of impedance to include capacitors and inductors.

Consider a sinusoidal signal represented by a complex exponential: It is a common shorthand to use "s" instead of "jw".

An analysis of the filters implemented with resistors and capacitors

Now let us look at the voltage-current relationships for resistors capacitors and inductors. For a resistor ohms law states: For a capacitor we can also calculate the impedance assuming sinusoidal excitation starting from the current-voltage relationship: This means that at very high frequencies the capacitor acts as an short circuit, and at low frequencies it acts as an open circuit.

What is defined as a high, or low, frequency depends on the specific circuit in question. For an inductor, impedance goes up with frequency. It behaves as a short circuit at low frequencies, and an open circuit at high frequencies; the opposite of a capacitor.

However inductors are not used often in electronic circuits due to their size, their susceptibility to parisitic effects esp. A Simple Low-Pass Circuit To see how complex impedances are used in practice consider the simple case of a voltage divider. If Z1 is a resistor and Z2 is a capacitor then Generally we will be interested only in the magnitude of the response: Recall that the magnitude of a complex number is the square root of the sum of the squares of the real and imaginary parts.

This is obviously a low pass filter i. If Z1 is a capacitor and Z2 is a resistor we can repeat the calculation: This concept of a complex impedance is extremely powerful and can be used when analyzing operational amplifier circuits, as you will soon see.

Active Filters Low-Pass filters - the integrator reconsidered. In the first lab with op-amps we considered the time response of the integrator circuit, but its frequency response can also be studied. First Order Low Pass Filter with Op Amp If you derive the transfer function for the circuit above you will find that it is of the form: But what do we mean by low or high frequency?

We can consider the frequency to be high when the large majority of current goes through the capacitor; i.

Analog circuits

Since R1 now has little effect on the circuit, it should act as an integrator. High-Pass filters - the differentiator reconsidered. The circuit below is a modified differentiator, and acts as a high pass filter.

First Order High Pass Filter with Op Amp Using analysis techniques similar to those used for the low pass filter, it can be shown that which is the general form for first-order one reactive element low-pass filters.

Therefore this circuit is a high-pass filter it passes high frequency signals, and blocks low frequency signals. Band-Pass circuits Besides low-pass filters, other common types are high-pass passes only high frequency signalsband-reject blocks certain signals and band-pass rejects high and low frequencies, passing only signal areound some intermediate frequency.

The simplest band-pass filter can be made by combining the first order low pass and high pass filters that we just looked at.

However, this circuit cannot be used to make a filter with a very narrow band. To do that requires a more complex filter as discussed below.The resulting filters requires CFOA, resistors and capacitors and most of the capacitors are grounded. Furthe r- more, for thin film fabrication the use of grounded capacitors eliminates the etching process and reduces the.

filter contains components like resistors, capacitors and For this reason a correct analysis and synthesis of analog filters is difficult without the use of algorithm implemented.

In the. that were implemented in bygone eras with resistors, capacitors, and inductors may now be implemented solely with resistors, capacitors, and op amps. The accuracy of these filters is ciently accurate and more amendable to a mathematical tractable analysis.

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This discussion SWITCHED CAPACITOR THEORY 3. of electronic (digital) trimming of multiple resistors and capacitors, the chip area must accommodate a growing number of components as the tuning range is increased and the . In Lab 6, a simple instrumentation amplifier was implemented and tested.

Lab 7 expanded upon the Resistors 9) Capacitors 10) Dual operational amplifier (UA) PRELAB: 1. Print the Prelab and Lab8 Grading Sheets.

Answer all of the questions in the Prelab Grading Active filters produce good performance characteristics, very good accuracy. Passive implementations of linear filters are based on combinations of resistors (R), inductors (L) and capacitors (C).

These types are collectively known as passive filters, because they do not depend upon an external power supply and/or they do not contain active components such as transistors.

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