National Instruments 370753C-01 Manual De Usuario

Each of these contributes a phase angle 

φ defined by:

with 

ω and p

 expressed in the same units, either radians per second or Hz, 

and using a four-quadrant arctangent function similar to that provided by 

atan2( )

 in Xmath. Thus the amount of phase contributed by a first order 

pole at the frequency

(generally termed the corner frequency, because the asymptotes used to 
draw different portions of the response intersect and form a corner) is –45

°. 

At frequencies beyond the corner frequency, the phase angle contributed by 
that pole comes closer and closer to –90

°. First-order zeros contribute phase 

angle in the same manner except that the sign of the angle is positive. 

[gnMargin,phMargin,dPdF,dGdF] = margin(H)

The 

margin( )

 function is a useful tool for evaluating the stability margin 

of a given system based on its frequency response. It returns PDMs 
indicating the gain margin and the phase margin, as well as the rate of 
change of gain and phase.

margin( )

 is defined for SISO systems only. It takes as input either a 

single PDM representing frequency response or a pair of PDMs containing 
gain information in decibels and phase information in degrees. In either 
case, the domain of the input is the set of frequency points, 

ω. 

Within 

margin( )

, as within 

bode( )

, the frequency response is 

converted to decibel magnitude and degree phase. All angles are converted 
to four-quadrant angles between 0

° and 360°. Use the following notation 

for each point i in the frequency range:

φ

ω p

⁄

(

)

atan

=

ω

=

Δx

x i 1

+

(

) x i

( )

–

=