Generating an amplified sine wave from a triangle wave using active circuit to create transfer function.
Derivative of sine is cosine. In cosine, from t = 0 to t = 90 deg or pi/2, cosine is decreasing until it reaches zero at t = 90 deg. This means the gradient (or derivative) of sine is decreasing from t = 0 to t = 90 deg. But sine is increasing on that interval. So…
We build a transfer function that exhibits similar behaviour. So on the positive swing, the idea is whenever sine is increasing, the rate at which it increases decreases. While the rate at which it decreases increases. This behaviour is reversed on the negative swing.
-> Let’s look at the following interval [v1, v4] (on
sine’s positive swing) and say we observe sine
increasing along this interval.
-> Let’s split the interval into two consecutive
intervals [v1, v2] and [v3, v4] within the
interval. The idea is the rate of increase
between [v1, v2] is higher than the rate of
increase between [v3, v4].
-> So we build a circuit that reduces the slope of
transfer function after every consecutive
interval up until we reach the peak of the
triangle wave where the derivative should be
zero. Then we mirror this behaviour on the
negative negative swing.
The interval was split into three. No rigorous calculations were carried out to determine the slope for each interval that will make the output closely resemble a sine wave. I however, made sure the slopes were lower for each consecutive interval. Output will still look somewhat like a sine wave.
The zener diodes set up the interval cut-off points while the feedback resistors set-up the slopes on each interval.
