Mathematical Expressions Useful for Tunable Properties of Simple Square Wave Generators

This paper compares two electronically controllable solutions of triangular and square wave generators benefiting from a single IC package including all necessary active elements (modular cells fabricated in I3T 0.35 µm ON Semiconductor process operating with ±1.65 V supply voltage). Internal cells are used for construction of building blocks of the generator (integrator and Schmitt trigger/comparator). Proposed solutions have adjustable parameters dependent on the values of DC control voltages and currents. Attention is given to the mathematical expressions for the advantageous tunability of these generators. Theoretical mathematical functions comparing the standard linear formula with special expression for the frequency adjustment are evaluated and compared with experimentally obtained results. Mathematical functions prove that the proposed topologies improve efficiency of tunability and reduce overall complexity of both generators. Features of proposed solutions were verified experimentally. Both single-parameter tunable designs target on the operation in bands from tens to hundreds of kHz (from 13 kHz up to 251 kHz for the driving voltage between 0.05 V and 1.0 V for the first solution; from 12 kHz up to 847 kHz for the driving current between 5 µA and 140 µA for the second solution). A comparison with similar solutions indicates beneficial performance of the proposed solutions in tunability ratio vs. driving parameter ratio and also because simplicity of circuitry is low. The qualitative evaluation and comparison of parameters of both circuits is given and confirms theoretical expectations.