# Schmitt Trigger Oscillator

The circuit shown below is a Schmitt trigger RC oscillator using a digital Schmitt trigger
inverter gate. The digital Schmitt trigger gate has a built-in hysteresis (0.8V) and the threshold voltages are V_{T+} (1.6V) and V_{T-} (0.8V). R1 connects the circuit in a positive feedback loop necessary for oscillation.

- When the Vc is less than V
_{T-}, Vo goes high (3.4V) and starts charging the capacitor C1 through R1.
- When Vc crosses the threshold voltage V
_{T+}, Vo goes low (0.2V) and discharging of C1 through R1 begins.
- When Vc crosses the threshold voltage V
_{T-}, step 1 is repeated. Thus the oscillating output is created.

Voltages are the typical values given by the 74LS14 specification.

Using the 74LS14, the output frequency is given by the following equation

\begin{equation}
f_o = {0.8 \over R_1 C_1}
\end{equation}

Using the values R1 = 1KΩ and C1 = 3.3μF (3300nF)

\begin{equation}
\begin{split}
f_o & = {0.8 \over 1 \times 10^3 \times 3.3 \times 10^{-6}} \\
& = 242 Hz
\end{split}
\end{equation}

## Application

To get an approximate 60Hz clock, add a Divide-by-4 Ripple Counter at the output of this Schmitt trigger RC oscillator.

By adding a divide by 16 and then a divide by 15 counter (divide by 240, 16*15=240), you can obtain a 1Hz clock frequency. Please go to truncated ripple counter to learn how to implement these counters.

## Circuit Analysis

To derive the frequency equation of a 74LS14 schmitt trigger oscillator, we will make use of the universal time constant formula for the RC circuit.

\begin{equation}
change = (final-start)( 1 - e ^ {-{t \over RC}})
\end{equation}

where
*change* is the capacitor voltage change
*final* is the capacitor voltage at infinity
*start* is the initial voltage of the capacitor

For t_{h} (the period when output is high), the capacitor is charged from 0.8V to 1.6V through the resistor from an output of 3.4V. Thus

- Change = 0.8V
- Start = 0.8V
- Final = 3.4V

\begin{equation}
\begin{split}
0.8 &= (3.4-0.8)( 1 - e ^ {-{t_h \over RC}}) \\
0.692 &= e ^ {-{t_h \over RC}} \\
ln (0.692) &= ln(e ^ {-{t_h \over RC}}) \\
-0.37 &= -{t_h \over RC} \\
t_h &= 0.37 RC
\end{split}
\end{equation}

For t_{l} (the period when output is low), the capacitor is discharged from 1.6V to 0.8V through the resistor from an output of 0.2V. Thus

- Change = -0.8V
- Start = 1.6V
- Final = 0.2V

\begin{equation}
\begin{split}
-0.8 &= (0.2-1.6)( 1 - e ^ {-{t_l \over RC}}) \\
0.428 &= e ^ {-{t_l \over RC}} \\
t_l &= 0.85 RC
\end{split}
\end{equation}

Total period of the output is

\begin{equation}
\begin{split}
t &= t_l + t_h \\
&= ( 0.85 + 0.37 ) RC \\
&= 1.22 RC \\
&= {RC \over 0.82}
\end{split}
\end{equation}

And after rounding down the constant, the frequency is

\begin{equation}
f = {1 \over t} = {0.8 \over RC}
\end{equation}