RC Filters | Sensor & Industrial Instrumentation - Electronics and Communication Engineering (ECE) PDF Download

RC Filters

Passive networks using resistors and capacitors are extensively used [2], and sometimes small inductors are used in instrumentation circuits for filtering out noise, frequency selection, and frequency rejection, and so forth.

Filters can be either passive [3] or active (using amplifiers), and are divided into the following types:

• High-pass: Allows high frequencies to pass but blocks low frequencies;

• Low-pass: Allows low frequencies to pass but blocks high frequencies;

• Band-pass: Allows a specific range of frequencies to pass;

• Band reject: Blocks a specific range of frequencies;
• Twin – T: Form of band reject filter, but with a sharper response characteristic.

Figure 3.7(a) shows a first order and second order low-pass RC filter [4], which passes low frequencies and rejects high frequencies, as shown in the frequency response curve in Figure 3.7(b). The cutoff frequency (_fc) of a filter is defined as the frequency at which the output power is reduced to one-half of the input power (−3 dB, or the output voltage is 0.707V_in). In the case of the first order low-pass filter, the cutoff frequency is given by:
f_c = 1/2πRC.........(3.13)

In the case of the second order low-pass filter, the cutoff frequency is given by:

The output voltage drops off at 20 dB/decade with a first order filter, 40 dB/decade for a second order filter, 60 dB/decade for a third order filter, and so forth. There is also a phase change associated with filters: −45° for a first order filter, −90° for a second order filter, −135° for a third order filter, and so forth. The phase change can cause instability in active circuits [5].
The input to output voltage ratio for any frequency (f) for a first order low-pass filter is given by:

The circuit for a high-pass, band-pass, and twin-T passive filters are shown in Figure 3.8. The number of resistive and capacitive elements determines the order of the filter (e.g., first order, second order, and so forth). The circuit configuration determines the characteristics of the filters, such as Butterworth, Bessel, Chebyshev, and Legendre. Figure 3.8(d) shows the frequency characteristics of the filters shown in Figure 3.8(b–c) [6].
These are examples of the use of resistors and capacitors in RC networks. Further descriptions of filters can be found in electronic textbooks [7].
Figure 3.8 (a) Low-pass filters, (b) High-pass filters, (c) band-pass filters, and (d) Band- reject