A P P L I C A T I O N S
Now, the region between 1 0 0 Hz and 4 0 0 Hz in Fig. 1 3
s h o w s a rise from poor low-frequency ( 1 0 0 0 Hz to 1 kHz)
response to a flattening out from beyond 1 0 0 0 and
4 0 0 0 Hz. Therefore, <we c a n expect that the higher fre-
quency components in the 1 0 0 Hz square w a v e will be
relatively normal in amplitude and phase but that the low-
frequency components
"B"
in this same square w a v e will
be modified by the poor low-frequency response of this
amplifier (see Fig. 1 4 A ) .
If the amplifier were such a s to only depress the low fre-
quency components in the square w a v e , a curve similar to
Fig. 1 5 would be obtained. However, reduction in
amplitude of the components is ususally caused by a reac-
tive element, causing, in turn, a phase shift of the com-
ponents, producting the tilt a s s h o w n in Fig. 1 4 A .
Fig. 16 reveals a graphical development of a similarly tilted
square w a v e . T h e tilt is seen to be caused by the strong in-
fluence of the phase-shifted 3rd harmonic. It also becomes
evident that very slight shifts in phase are quickly s h o w n
up by tilt in the square w a v e . Fig. 17 indicates the tilt in
square w a v e produced by a 1 0 ° phase shift of a low-
frequency element in a leading direction. Fig. 1 8 indicates a
1 0 ° phase shift in a low-frequency component in a lagging
direction. T h e tilts are opposite in the t w o cases because of
the difference in polarity of the phase angle in the t w o
cases a s can be checked through algebraic addition of com-
ponents.
Fig. 1 9 indicates low-frequency components w h i c h have
been reduced in amplitude and shifted in phase. It will be
noted that these examples of low-frequency distoriton are
characterized by change in shape of the flat portion of the
square w a v e .
Fig. 1 4 B s h o w s a high-frequency overshoot produced by
rising amplifier response at the high frequencies. It should
again be noted that this overshoot makes itself evident at
the top of the leading edge of the square w a v e . The sharp
rise of the leading edge is created by the summation of a
large number of harmonic components. If an obnormal rise
in amplifier response occurs at high frequencies, the high
frequency components in the square w a v e will be amplified
larger than the other components creating a higher
algebraic s u m along the leading edge.
Fig. 2 0 indicates high-frequency boost in an amplifier a c -
companied by a lightly damped " s h o c k " transient. In this
c a s e , the sudden transition in the square w a v e potential
from a sharply rising, relatively high frequency voltage, to a
level value of low-frequency voltage, supplies the energy
for oscillation in the resonant network. If this network in
the amplifier is reasonably heavily damped, then a single
cycle transient oscillation may be produced as indicated in
Fig. 2 1 .
Fig. 2 2 summarizes the preceding explanations and serves
as handy reference.
F i g .
15- Reduction of square wave fundamental
frequency component in turned circuit
F i g .
16. Square wave tilt resulting from
3 r d
harmonic phase shift
F i g .
17. Tilt resulting from phase shift of funda-
mental frequency in a leading direction
17
F x
3
F x 3 O U T O F P H A S E ( L E A D )
F x
1
F X 1 OUT O F P H A S E ( L E A D )
