# 10. Band Pass Filters¶

## 10.1. Objective¶

The objective of this Lab activity is to:

1. Construct a Band Pass Filter by cascading a low pass filter and a high pass filter.
2. Obtain the frequency response of the filter using Bode analyzer application.

## 10.2. Notes¶

In this tutorials we use the terminology taken from the user manual when referring to the connections to the Red Pitaya STEMlab board hardware.

Bode analyzer application is used to measure frequency response of Low Pass and High Pass Filters.

The Bode analyzer is an ideal application for measuring frequency responses of the passive/active filters, complex impedances and any other electronic circuit. The Gain/Phase frequency response can be used to characterize any device under test completely, you can perform linear and logarithmic sweeps. Gain and Phase can be measured from 1Hz to 60MHz. The basic user interface enables quick interaction and parameter settings. The Bode analyzer can be used for the measurement of Stability of control circuits such as the DC/DC converters in power supplies, Influence of termination on amplifiers or filters, Ultrasonic and piezo electric systems and similar.

## 10.3. Background¶

A Band Pass Filter allows a specific range of frequencies to pass, while blocking or attenuating lower and higher frequencies. It passes frequencies between the two cut-off frequencies while attenuating frequencies outside the cut-off frequencies. One typical application of a band pass filter is in Audio Signal Processing, where a specific range of frequencies of sound are desired while attenuating the rest. Another application is in the selection of a specific signal from a range of signals in communication systems. A band pass filter may be constructed by cascading a High Pass RL filter with a roll-off frequency $$f_L$$ and a Low Pass RC filter with a roll-off frequency $$f_H$$, such that:

$f_L < f_H$

The Lower cut-off frequency is given as:

$f_L = \frac{R}{2 \pi L} \quad (1)$

The higher cut-off frequency is given as:

$f_H = \frac{1}{2 \pi RC} \quad (2)$

The Band Width of frequencies passed is given by:

$BW = f_L < f_{BW} < f_H \quad (3)$

All signal frequencies $$f$$ below $$f_L$$ and above $$f_H$$ are attenuated and the frequencies between are passed by the filter.

## 10.4. Frequency Response¶

To show how a circuit responds to a range of frequencies a plot of the magnitude ( amplitude ) of the output voltage of the filter as a function of the frequency can be drawn. It is generally used to characterize the range of frequencies in which the filter is designed to operate within. Figure 2 shows a typical frequency response of a Band Pass filter.

## 10.5. Materials:¶

• Red Pitaya STEMlab 125-14 or STEMlab 125-10
• Resistor: 1 KΩ
• Capacitor: 0.047 µF
• Inductor: 22 mH

## 10.6. Procedure¶

1. Set up the filter circuit as shown in figure 1 and figure 3 on your solderless breadboard, with the component values R1 = 1 KΩ, C1 = 0.047 µF, L1 =22 mH.

Figure 3: Band Pass Filter on solderless breadboard

2. Start the Bode analyzer application. The Bode analyzer application will make a frequency sweep in such way it will generate sine signal on $$OUT1$$ within frequency range selected by us(in settings menu). $$IN1$$ input signal is directly connected to $$OUT_1$$ following that $$IN1=V_{in}$$. $$IN2$$ is connected on the other side of the filter and from that $$IN2=V_{out}$$. Bode analyzer application will then for each frequency step take the ratio of $$IN1/IN2$$ ($$V_{in}/V_{out}$$) and calculate frequency response.

3. In the Bode analyzer settings menu set for:

• start frequency: 500 Hz
• end frequency: 30 kHz
• number of steps: 50
• scale: Log
• select RUN button

Figure 4: Band Pass Filter measured Frequency Response

## 10.7. Questions:¶

1. Compute the cut-off frequencies for each Band Pass filter constructed using the formula in equations (1) and (2). Compare these theoretical values to the ones obtained from the experiment and provide suitable explanation for any differences.