Taking apart a solar-powered lamp revealed a single-transistor voltage converter circuit that allowed an LED to be driven from a 1.2 V cell. The l/h diagram shows the circuit (with slight modifications). The circuit oscillates at about 500 kHz and, at a cell voltage of 1.4 V, draws 11 mA with a respectably bright LED. The circuit works down to a supply voltage of 0.8 V.
Understanding the Series Resonant Circuit
The oscilloscope display confirms the expected 3 Vpp output at the LED. The left-hand coil and the capacitor together create a series of resonant circuits, triggered by the periodic alternation between conduction and blockage of the transistor’s collector. During the transistor’s conducting phase, the upper coil discharges its stored energy, causing the collector voltage to rise to approximately double the cell voltage.
Analyzing Phase Shift in Resonant Circuit
A surprising 35 Vpp sine wave voltage across the capacitor within the resonant circuit was observed. Employing a two-channel oscilloscope allowed the assessment of phase relationships. The resonant circuit introduces a phase shift of about 90 degrees. Additional phase shifts are contributed by the base resistor, base capacitance, and the transistor’s Miller capacitance, as detailed in the Miller effect (http://en.wikipedia.org/wiki/Miller_effect).
Utilizing Series Resonant Circuit for Voltage Conversion
The amplified voltage from the series resonant circuit can be harnessed for various applications, such as constructing a bipolar voltage converter, particularly useful for powering low-power operational amplifiers (see r/h diagram). This setup involves two electrolytic capacitors and two diodes that rectify the voltage. The resulting circuit can yield a voltage difference of 9 V at 0.2 mA, adequate for operating a low-power opamp.
Sine Waves: Mathematical Representation and Applications
A sine wave, also known as a sinusoidal wave. It is a mathematical curve described by the sine trigonometric function. Represented by the equation y = sin x. It is a smooth periodic function oscillating above and below zero. Sine functions and sine waves are widely employed in modeling economic and financial data characterized by cyclic or periodic patterns. Time serves as the variable in such modeling scenarios. For instance, businesses selling consumer discretionary goods often experience seasonal fluctuations in sales and revenues, making sine waves a valuable tool for analysis.