# High order Filters ($\ge$2nd order) Explanation

I am not understanding the outcome I have been getting with High order filters. It doesn't make sense to me. Ill explain it in cases and where I don't understand something.

Case 1:

R1 = R2 = 5.6

C1 = C2 = 1uF

Using online Calculator should have a Fc ~= 28420.525552124[Hz]

simulate this circuit – Schematic created using CircuitLab

Q: Where am I suppose to know where this Fc lies? -3dB - 6dB -9dB? I am assuming since this is a 2nd order filter it should contain the calculated Fc at -6dB.

Simulation:

How is it at -9dB, thought that characteristic is only present in 3rd systems?

Case 2:

simulate this circuit

Essentially there's a High Pass Filter at the + terminal with a Fc = 0.318Hz

and another HighPass filter at the NFB with Fc = 0.350Hz With the transfer function of: $$\ H(s)=\frac{V_{OUT}}{V_{IN}}= \frac{611s+100}{47s+100}\$$

I would expect the output of this amplifier to have a Fc at the high pass filter to be around 0.318Hz however its not. The only thing I know is the NFB is influencing the Fc but I dont know how.

Q:I thought the it would be isolated from each other. Also when I add another High pass filter at the output why does it change the Fc Again?

The output of the Amplifier above.

• As to your first schematic: if you cascade the same components that will not give you the same cut-off frequency. – Oldfart Nov 8 at 20:26
• In case 1: It did thought but at a much different roll off Frequency? If not why did the online calculator suggest otherwise? – Pllsz Nov 8 at 20:29
• The corner frequency is considered at half power, or 1/sqrt(2) usually (save for exotic more transfer functions). If it's a 10th order filter, it will not be at a multiple of -3dB, but at -3dB. You are directly cascading same valued sections, each one will influence the previous, search for Cauer topology, it's an entire theory. Also, even if they didn't, repeating same sections (synchronous tuning) leads to repeated convlution with the same kernel which converges towards a Gaussian. – a concerned citizen Nov 8 at 20:31
• Then why isn't in Case 1: The Fc at -3dB but at ~-9dB? – Pllsz Nov 8 at 20:38
• Because you are calculating the filter wrong. As Oldfart said, each stage loads the other one and the filter poles interact with each other. You cannot simply use a 1st-order calculation and put two of them together. – Edgar Brown Nov 8 at 21:43