Examples

A acquiescent (unity canyon bandage gain) lowpass RC filter, for instance has the afterward alteration action bidding in the abundance domain:

From the alteration action it can be bent that the blow abundance point fc (in hertz) is at the frequency

or (equivalently) at

area is the angular blow abundance in radians per second.

The alteration action in agreement of the angular frequencies becomes:

The aloft blueprint is the normalized anatomy of the alteration function. The Bode artifice is apparent in Figure 1(b) above, and architecture of the straight-line approximation is discussed next.

editMagnitude plot

The consequence (in decibels) of the alteration action above, (normalized and adapted to angular abundance form), accustomed by the decibel accretion announcement :

when advised against ascribe abundance on a logarithmic scale, can be approximated by two curve and it forms the asymptotic (approximate) consequence Bode artifice of the alteration function:

for angular frequencies beneath it is a accumbent bandage at 0 dB back at low frequencies the appellation is baby and can be neglected, authoritative the decibel accretion blueprint aloft according to zero,

for angular frequencies aloft it is a bandage with a abruptness of −20 dB per decade back at top frequencies the appellation dominates and the decibel accretion announcement aloft simplifies to which is a beeline bandage with a abruptness of −20 dB per decade.

These two curve accommodated at the bend frequency. From the plot, it can be apparent that for frequencies able-bodied beneath the bend frequency, the ambit has an abrasion of 0 dB, agnate to a accord canyon bandage gain, i.e. the amplitude of the clarify achievement equals the amplitude of the input. Frequencies aloft the bend abundance are attenuated – the college the frequency, the college the attenuation.

editPhase plot

The appearance Bode artifice is acquired by acute the appearance bend of the alteration action accustomed by

versus , area and are the ascribe and blow angular frequencies respectively. For ascribe frequencies abundant lower than corner, the arrangement is baby and accordingly the appearance bend is abutting to zero. As the arrangement increases the complete amount of the appearance increases and becomes –45 degrees if . As the arrangement increases for ascribe frequencies abundant greater than the bend frequency, the appearance bend asymptotically approaches −90 degrees. The abundance calibration for the appearance artifice is logarithmic.

editNormalized plot

The accumbent abundance axis, in both the consequence and appearance plots, can be replaced by the normalized (nondimensional) abundance arrangement . In such a case the artifice is said to be normalized and units of the frequencies are no best acclimated back all ascribe frequencies are now bidding as multiples of the blow abundance .