INTRODUCTION

1. To study the bandpass filter in the case of RLC circuit2. To study the effect of source resistor, Ri on the performance of bandpass filter3. To introduce the frequency response of the bandpass filter4. To establish the bandpass characteristic

THEORETICAL PART

Filters An ideal filter is a network that allows signals of only certain frequencies to pass while blocking all others. Depending on the regime of frequencies that are allowed through or not they are characterized as low-pass, high-pass, band-pass, band-reject and all-pass. There are many needs for electric filters, some of the more common being those used in radio and television sets, which allow tuning in a certain channel by passing its band of frequencies while filtering out those of other channels. The frequency response is divided into magnitude (amplitude) and phase parts. The amplitude curve of a filter will indicate how closely the practical circuit imitates the ideal filter characteristics that are as follows:

Filter operation is considered when the amplitude of the output signal of the circuit is relatively large for some frequencies and small for others. Then one can say that for the former the signal passes and for the latter it does not.

Bandpass Filter

Band pass filters can be constructed by combining a low pass filter in series with a high pass filter as shown in the figure above. These are often used in instrumentation to filter out low and high frequency noise, and also as part of a demodulation instrument to extract one channel of data. Example, we use bandpass filter to tune in the radio station

A band pass filter is a device that passes frequencies within a certain range and rejects (attenuates) frequencies outside that range.

The characteristic of a band pass filter or any filter for that matter is its ability to pass frequencies relatively unattenuated over a specified band or spread of frequencies called the pass band. For a low pass filter this pass band starts from 0 Hz or DC and continues up to the specified cut-off frequency at - 3 dB down from the maximum pass band gain. Equally for a high pass filter the pass band starts from this - 3 dB cut-off frequency and continues up to infinity or the maximum open loop gin an active filter.

However the active Band Pass filter is slightly different in that it is a frequency selective filter circuit used in electronic system to separate a signal at one particular frequency, or a range of signals that lay within certain band of frequencies from signals at all other frequencies. This band or range of frequencies is set between two cut-off or corner frequency points labeled the lower frequency (fL) and the higher frequency (fH) while attenuating any signals outsides of these two points.

An ideal band pass filter would have a completely flat bandpass (with no gain/attenuation throughout) and would completely attenuate all frequencies outside the bandpass. Additionally the transition out of the bandpass would be instantaneous in frequency. In practice, no bandpass filter is ideal. The filter does not attenuate all frequencies outside the desired frequency range completely: in particular, there is a region just outside the intended Passband where frequencies are attenuated, but not rejected. This is known as roll-off, and it is usually expressed in dB of attenuation per octave or decade of frequency. Generally, the design of a filter seeks to make the roll-off as narrow as possible, thus allowing the filter to perform as close as possible to its intended design.

The bandwidth of the filter is simply the difference between the upper and lower cut-off frequencies. The shape factor is the ratio of band widths measured using two different attenuation values to determine the cut-off frequency.

A band pass filter can be characterized by Q-factor. The Q-factor is the inverse of the fractional band width. A high Q-filter will have a narrow bandpass and a low Q-filter will have a wide bandpass.

Bandpass characteristic

METHODOLOGY

Frequency ResponseH =

Centre Frequency/ Resonant Frequency = 0 = =

max = = =

Cut off frequency

Lower cut off frequency

Higher cut off frequency

= If Ri = 0, =

Quality FactorQ = = =

Transfer Function of Bandpass FilterV0 (s) = I(s)R = = = = H(s) = = =

Result and discussion