# Confusion with cut-off frequency calculation using Thevenin equivalent of an RC low pass filter

When I was trying to see the effect of load at the output of an RC low-pass filer I found myself in some sort of confusion. Below is an RC low-pass filter circuit with another R as a load and its Thevenin equivalent:

LTspice simulation in time domain shows that these circuits are giving same outputs at any frequency. Therefore I thought the cut-off frequency of the Original circuit must be the same as its Thevenin equivalent.

To verify it I first plotted the frequency response of the Original circuit as below:

As you see in the above plot, the Vout starts from -6dB and there is no -3dB in the entire plot for a cut-off frequency.

Then I plotted the frequency response of the Thevenized equivalent as below:

Above plot shows the -3dB point corresponds to 2.3Hz cut-off frequancy.

And finally I used the cut-off formula fc = 1/(2 * pi* R * C) for the Thevenized equivalent circuit and found fc = 31.8Hz.

What is going on wrong here?

All three ways give different results. Which one is the right one?

• I think you're looking at the phase not the gain in the second plot. Use the same horizontal axis settings as the first plot. The first plot has 6dB loss because of the 2:1 attenuator - which will be the same voltage as the V source in the second. You're interested in the -3dB point relative to that loss, i.e. -9dB.
– user16324
Commented Jul 15, 2016 at 11:48
• I see, but I still dont get why the first plot starts from -6dB. Commented Jul 15, 2016 at 11:55
• Quote: "As you see in the above plot, the Vout starts from -6dB and there is no -3dB in the entire plot for a cut-off frequency." REMEMBER: The cut-off frequency is defined as a frequency where the ouput is 3 dB less than the output at DC.
– LvW
Commented Jul 15, 2016 at 11:56
• Because the two resistors halve the input voltage, which is 6dB loss. In the Thevenin circuit you have no similar loss, you turn the source voltage down by 6dB instead.
– user16324
Commented Jul 15, 2016 at 12:07
• @LvW your definition of cut-off relieved my pain i was blindly looking for -3dB Commented Jul 15, 2016 at 12:14