# Why is the closed gain loop -3dB from the open loop gain rather than some other value?

I am reading the book Op Amps for Everyone and in the chapter of feedback loop theory, I have this quote (see picture) where it says in reality the closed loop gain is down by 3dB at the point X as shown below.

How does he know it is -3dB and not some other value that is proportional to the gain B?

page number 85, link to the book:Op Amps for Everyone

• The -3dB point is by definition the point at which we read the frequency (x-axis) to determine the bandwidth. It is the same as with a simple RC filter, a 1 kHz lowpass filter has an attenuation of -3 dB at 1 kHz. If your simple RC filter attenuates -1 dB at 1 kHz then it's not a 1 kHz filter! So the author doesn't somehow "know" it should be -3 dB, instead it is a standard way to define the bandwidth. – Bimpelrekkie Jan 15 at 13:25
• so he refers directly to cut off frequency. Thanks – Yaakov Jan 15 at 13:53

The text says it's a single pole amplifier circuit and that always means that at the cut-off frequency, due to the transfer function gain equation, the output signal is down to exactly half the power of the input signal. Half the power in decibels is $$\10\log_{10}(0.5) =\$$ -3.0103 dB.

That's what single pole filters do at their cut-off frequency.

• The order of the LPF is irrelevant to the defined amplitude response BW at -3dB !! Not because it is a single pole !! kinda misleading. – Tony Stewart Sunnyskyguy EE75 Jan 17 at 18:05
• I'm just describing a single pole filter. If I said that all boys have two biological parents would I be wrong? Of course, the bigger picture is that everyone has two parents. – Andy aka Jan 17 at 18:14
• so could someone infer a 2nd order filter is -6dB ? yes if they cascaded two same 1st order , no the BW is defined by -3dB and thus BW will be reduced. See the ambiguity it might cause? But you might be a test tube baby (lol) – Tony Stewart Sunnyskyguy EE75 Jan 17 at 18:24
• My sister is Louise Brown... Well actually she's called Louise and our shared surname begins Br.... so that's near enough for me. – Andy aka Jan 17 at 18:29
• The closed loop gain will be 3 dB lower but at a much higher frequency. If I’ve not been clear, leave another message and I’ll try again tomorrow @Yaakov – Andy aka Feb 2 at 0:42

ALL filters regardless of type, shape or order are defined by the half-power points in the passband or -3.01 dB or 0.707 V. This is simply the amplitude response by definition defined by half-power.

But, there are many other complex filters that have more important specs like linear-phase or group-delay flatness to -6 or -12 dB or PB ripple in dB using higher Q offset f for steep skirts or band stop BW and attenuation. For Chebychev Filters the skirts are steeper by staggering higher Q filters and the equal ripple filter is defined by the BW limited by the ripple in the band and where it exceeds this dB ripple at the edge, which is more important than the half-power point. (ty LVW)

This is why no other value is used for basic passband amplitude response.

• Just for the sake of exactness: All Chebyshev and Cauer (elliptical) responses have a path band which is defined by the ripple within this band (and NOT by half-power points). – LvW Jan 15 at 16:27
• Yes but the ripple BW is separate from the amplitude response BW, so these are defined by both parameters – Tony Stewart Sunnyskyguy EE75 Jan 17 at 16:20
• I don`t think that - for Chebyshev and Cauer responses - we have two different pass band definitions at the same time. Look at the pole parameter tables in relevant books and/or study the filter design programs - all use the ripple properties for defining the passband. And this makes much sense!! Mote than that, in some cases, for the Bessel response the passband edge is defined in the time domain (group delay flatness). – LvW Jan 17 at 17:40
• Again multiple specs for complex filters. I design Bessel for the range in dB like -6dB or -12dB and Cheb by dB and Linear phase to 2ndary BW and deg. then Raised Cosine to Q but Amplitude response remains the same fo= -3dB where BPF have 2 such points. When Cheb ripple becomes 0dB it is a Butterworth – Tony Stewart Sunnyskyguy EE75 Jan 17 at 17:55
• I must admit that I have problems to regard your comment as an answer to my comment. Therefore, one single clear and simple question: Do you agree that there is a common understanding (which is reflected in all the available filter tables) that the passband edge of a Chebysheff lowpass of any order is defined by the (last occurence of the) allowed passband ripple? For example: 0.1, 0.5 or 1 dB? – LvW Jan 17 at 18:10