less than 1,000 pF. What are the other
1) The logic gate has no well-defined
input thresholds. Near an input
voltage of approximately Vcc/2, this
alleged digital device behaves as a
high-gain linear amplifier. Normally,
this input region is transitioned very
rapidly in pure interconnected logic
and is not a problem, but when
passive components are added as
loads, this may not be the case.
FIGURE 2. A classic ring oscillator.
has been used for the [R1,C1] tank
circuit to transfer the switching edges
of the output to the input without additional phase lag through the capacitor.
There is a price to pay for this: slow
slew rate near Vcc/2, as noted above.
Note that the observed propagation
delays are actually less than specified.
The Ring Oscillator With
a Tank Circuit
2) Since passing through the input “no
man’s land” near Vcc/2 must be done
rapidly, each CMOS logic family has a
minimum input slew rate requirement.
For example, the 74HC family
specifies a fast rise time of at least 11
volts/microsecond. This is not a problem when gates of the same family are
interconnected directly, but addition
of an RC tank circuit imposes slower
ramps near Vcc/2 as shown in the
Figure’s timing diagram at node VFB,
at times A and B. Here the form of the
circuit forces a slow decay near the
input transition points, with a slew rate
of only .022 volts/microsecond for the
values shown. Although the gate tolerates this, we are asking for trouble.
You will often find a very high frequency burst oscillation at VFB, points
A and B, for a few microseconds.
Further, any noise on the output,
typically from the power and ground
rails, is fed back to node VFB through
C1 — producing frequency jitter,
known as phase noise. Of course, one
can employ a slower logic family, such
as first generation 4000 CMOS digital
logic, which has a slower minimum
input slew rate, but this approach
attempts to compensate for a defect
in the form of the circuit with a lack of
performance of the logic gate.
in RC Relaxation
A comprehensive representation
for understanding high speed digital
gates includes propagation delay.
Consider Figure 2, where we see three
inverters in series. I have used Schmitt
inverters here to give a crisp threshold
action and prevent spurious oscillations.
When Vcc is applied to the circuit,
noise and drift at the inputs will initiate
stable oscillation directly after a short
transient interval. Since each gate has
a response time — or propagation
delay — of about 15 nanoseconds, we
will see at VOUT a 45 nanosecond
pulse ( 3 x 15 nanoseconds) that will
travel continuously around the loop,
with a spacing of 45 nanoseconds,
producing an output frequency near
11 MHz — without any RC tank circuit
whatsoever! We have a classic, free
running “ring” oscillator.
The propagation delay sets an
upper limit to the frequency of oscillation, since addition of RC elements to
the feedback will lower this frequency
to practical values well below this. Build
the actual circuit in Figure 2 and try it!
A superior oscillator to Figure 1
can be achieved by adding an RC tank
circuit to the ring oscillator of Figure 2,
as shown in Figure 3. Note that the
resistor and capacitor have been
swapped in position, but are still commutated between the outputs of the
last two inverters. Now the output has
a DC path to the input. As in Figure 1,
the differentiating circuit allows a non-Schmitt inverter to again be used. This
is a better form than Figure 1, but rather
than invest time on designing to it, let’s
move on to an even better oscillator.
A Better Oscillator
Refer to Figure 4. Of course, we
can always realize a utility oscillator
using the CMOS 555 timer, but this
can be expensive. Your design may
have leftover NOT and NAND Schmitt
gates that can be usefully employed.
Note that RC relaxation oscillators that
employ digital logic gates are not
precision devices and are without tight
tolerances on frequency. They are generally suitable only for utility clocking.
Figure 4 details a simple oscillator
that uses only one NAND gate within
a 74HC132 quad Schmitt NAND
integrated circuit. An inverter within a
3) An even number of gates have
been used to produce 360 degrees
of overall phase shift and induce
oscillation. This requires that the RC
tank circuit should introduce no additional phase shift in the feedback loop
— accordingly, a differentiating circuit
FIGURE 3. A ring oscillator
with tank circuit.
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