‘Bootstrap’ Ramp GeneratorFor many purposes, for example providing a time axis for oscilloscope displays, a
voltage varying linearly with time is needed. In many instances a satisfactory
approximation to such a 'ramp' is obtained by making use of a simple RC charging
circuit, using just the initial part of the exponential charging response. For a time
interval small compared to the RC time constant the exponential is well approximated
by a tangent at the origin. Modifications of this basic procedure improve in one way or
another the linearity of the approximation or, perhaps more accurately said, extend the
period over which the approximation is useful. Several ‘ramp’ circuits are reviewed in
this note.
Basic RC Ramp
A straightforward approach to generating a ramp
voltage is illustrated by the circuit diagram to the right.
A square wave applied to the BJT alternately switches
the transistor between saturation and cutoff operation.
When the transistor is cutoff the capacitor C1 charges
exponentially through R2, with a time constant R2 C1.
On the other hand if the transistor is turned on the
capacitor discharges rapidly and the transistor saturates.
The transient response of this circuit was computed for
two conditions. The data plotted immediately below is
for a pulse width of 1 millesecond and a period of 30
millesecond. The period is several time constants in
width so as to make the exponential nature of the RC
charging clearly evident.
Only the initial part of the
exponential rise, a period
short compared to one time
constant,, is ‘linear’ to any
extent.
In practice the pulse
duration would be
considerably shorter, just
long enough allow for just
the initial part of the
charging cycle. To illustrate
this the circuit response was
recomputed, this time for a
pulse width of 50 μseconds and a period of just 0.5 millesecond, about one tenth the time constant. The
computed data is plotted below. Comparison of the computed data with expected performance is left as
an exercise.