- #1

topcat123

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## Homework Statement

3. FIGURE 3(a) shows a simple low-pass filter followed by a buffer

amplifier.

(a) Write down the transfer function for the filter.

(b) Determine the 3db frequency (fc) if R = 10 kΩ and C = 10 nF.

(c) If four such stages are cascaded as shown in FIGURE 3(b),

determine the gain and phase of the overall transfer function at

(i) 0.1fc

(ii) 10fc.

## Homework Equations

The Transfer function

[tex]\frac{V_{out}}{V_{in}}=\frac{-1}{1+j\frac{{\omega}}{{\omega}_c}}[/tex]

The natural frequency at -3dB

[tex]f_c=\frac{1}{2{\pi}RC}[/tex]

## The Attempt at a Solution

a) as above the transfer function

b)[tex]f_c=\frac{1}{2{\pi}RC}=\frac{1}{2{\pi}10000*10*10^{-9}}=1.59KHz[/tex]

c) I am a bit stuck with this one

I know

The resulting RC filter circuit would be known as an “nth-order” filter with a roll-off slope of “n x -20dB/decade”.

So the roll off of this 4th order filter would be -80dB

The phase shift for a single low pass filter is[tex]-arctan(2{\pi}fRC)=-arctan(\frac{f}{f_c})[/tex]I am asuming that the phase shifts of all 4 can be added?

All help is apreciated

Thanks