
effG
R=T
¼ffG
R=T
(e
jvT
) ffG( jv)(8:400)
¼ Arg
b
1
e
jvT
þ b
0
e
jvT
(e
jvT
a
0
)
Arg
1
jv l
(8:401)
¼ Arg
b
1
e
jvT
þ b
0
(e
jvT
a
0
)
vT Arg
1
jv l
(8:402)
¼ e
ffG
vT (8:403)
The fractional gain and phase errors for the classical and real-time, improved Euler integrators are
graphed in Figure 8.87 for the case when l ¼0.5. As expected from Equation 8.397, the fractional
gain errors are equal and from Equation 8.403, the real-time, improved Euler integrator introduces
an additional phase lag of vT rad. Note that the fractional gain error varies from zero to approxi-
mately 2% over the interval 0 vT 0.5 rad.
Also, note that e
ffG
0 for 0 v vT 0.5 rad. Hence,