3dB drop point is a good measure to decide whether we are within or outside the pass band of a filter/system.

Let's consider a basic 1st-order RC low-pass filter.

For sufficiently low frequencies (when R > |Zc|) the magnitude of the gain is almost 0 (actually changes (drops) continuously with frequency at a rate of -20dB/dec).

Zc is the impedance of C, whose magnitude is |Zc|=1/(wC).

(w=2pi*f is the angular frequency)

Obviously, for w1/RC it is 0 (actually is a pure "complex" gain inversely porportional with frequency; i.e. drops continuously).

So, 1/RC value is a good metric for us to decide whether we are within the pass band or outside. At w=1/RC the magnitude of the gain is 0.707 (1/√2) which is approximately -3dB.

Therefore, it is convenient to define the "3dB gain drop point(s)" as the "corner(s)" of a passband, which determine the bandwidth (3dB bandwidth).

This convention of 1st-order systems is usually preferred in higher-order systems as well.

The 3dB bandwidth is referred to because, for first order systems, it is easy to calculate and because it corresponds to the discontinuities in the piecewise linear approximation of the Bode plot

3dB drop point is a good measure to decide whether we are within or outside the pass band of a filter/system.

Let's consider a basic 1st-order RC low-pass filter.

For sufficiently low frequencies (when R > |Zc|) the magnitude of the gain is almost 0 (actually changes (drops) continuously with frequency at a rate of -20dB/dec).

Zc is the impedance of C, whose magnitude is |Zc|=1/(wC).

(w=2pi*f is the angular frequency)

Obviously, for w1/RC it is 0 (actually is a pure "complex" gain inversely porportional with frequency; i.e. drops continuously).

So, 1/RC value is a good metric for us to decide whether we are within the pass band or outside. At w=1/RC the magnitude of the gain is 0.707 (1/√2) which is approximately -3dB.

Therefore, it is convenient to define the "3dB gain drop point(s)" as the "corner(s)" of a passband, which determine the bandwidth (3dB bandwidth).

This convention of 1st-order systems is usually preferred in higher-order systems as well.

Because at that frequency the power of the output is half the power of the input. As Ali Zeki explained above the -3dB point is that where the amplitude falls to 1/√2), hence the power falls to 1/2.

3dB bandwidth refers to half power bandwidth, where as in communication and antenna designs 90% power bandwidth( which is much less than 3dB bandwidth) is preferred one over 3dB bandwidth

I agree with Mr.Fernando and Mr.Vijay

These rule of thumb parameters let you aim the antenna for best effect (or least harm) in an application. These measures also simplify complicated design issues with gain and directionality. A small angle is very directional but will have a high gain and a large angle gives a low gain.

The half power version in the OP gives a really close estimate of the significant signal output beam, the beam will null out just a few degrees wider at the cutoff angle. Mr Chakka's measure will give the direction where signal is at its full power. Picture a dartboard with a middle ring at 90%, the easy to hit rings are 50%, and edge of board is 0%.

@Imitiyaz

Have you arranged your answer from different internet sites?

:-)

E.g.

http://tinyurl.com/lcec3jh

http://tinyurl.com/mmeg2h5

Coz it refers to 1/2 power drop

@Vijay kumar Chakka Thank you for your answer, but I think Antenna is a spatial filter too. So, Antenna pattern is a spatial representation of radiated (received) power distribution taken in fourier domain (FT to change tinme to space domain). If the propagation channel exhibits non-linear phase velocity (k) we cannot directly comment on the signal bandwidth of the antenna. The case that you have focused on is same for signal bandwidth (to estimate any signal faithfully). However, I am asking for the reason for the term 3-dB beamwidth considering antenna as a spatial filter, which has an essence of a general filter.

The 3 dB, or half power, beamwidth of the antenna is defined as the angular width of the radiation pattern, including beam peak maximum, between points 3 dB down from maximum beam level (beam peak).

From the maximum power theorem , maximum power transferred form source to load when load resistance is equal to source resistance.

We hope the output of any system to be-at least- the same as the input

(lossless) , however, it is not the case in passive circuits, So, it is a kind of compromise between acceptable magnitude and bandwidth (BW) to accept a BW in which we lose nearly 30% of the magnitude and have a half power output. It is nearly the same as the root mean square (r.m.s) value measure of signals.

it's kinda a rule of thumb in which any power drop below the 3dB threshold (1/2 of the input power) is considered to be noise.

3dB bandwidth is the point at which the output power is half than input, this can be calculated mathematically as:

10 log10(1/2)

≈-3 dB