Cascading filters

Build the RC circuit shown in below, with $R_1=R_2=10kOhm, \space C_1=C_2=4.7nF$

Fig. 5: (left) schematic of the single stage RC circuit, (right) implementation on breadboard

Analysis

The claimed transfer function of this circuit is

Where  $j=\sqrt-1$ is the imaginary unit.

1. What is the magnitude of the transfer function?
2. What is the phase response of the circuit?
3. What class (low-pass, high-pass, band-pass, band-stop) of filter is this?
4. What is the -3dB frequency?

Measurement

Using the Red Pitaya’s Bode Analyzer tool, measure the frequency response (|T(f)|) as described in section 3.1.2.

1. Show the plot of the measurement below:

Comparison

Respond to the following questions:

1. Does the shape of the frequency response match your expectation from the analysis? Is there any point that stands out as odd?
2. Find the -3dB point in the circuit, and compare this value to the one you previously calculated.
3. This circuit can be viewed as two separate 1st order filters (see section 3.1) cascaded. What would the expected transfer function of such an arrangement look like? How different is this the expression you would expect from two ideal LTI systems?