Follow

Calculus

  • K7-41: RC CIRCUIT - DIFFERENTIATION AND INTEGRATION

    K7-41
    Demonstrate differentiation and integration using RC circuits.
    A series RC circuit is used to obtain the derivative or the integral of a periodic electronic signal. For differentiation the time constant of the series RC circuit must be very small compared to the period of the wave. The derivative is sensed as the voltage across the resistor (current in the circuit). For integration the time constant of the series RC circuit must be very large compared to the period of the wave. The integral is sensed as the voltage across the capacitor. Waves from a signal generator are input into the circuit, including sine wave, triangular wave, sawtooth, and square wave. The appropriate circuits are shown above.

    Note that these circuit elements are very small, and hard to see in a classroom. A camera may be requested to display them on screen in the large lecture halls.

    K7, ME2, ME3

  • K7-44: RLC CIRCUIT - 10KHZ - DIFFERENTIATION AND INTEGRATION

    K7-44
    Demonstrate differentiation and integration using an RC circuit.
    The resistance and capacitance from the packaged RLC resonant circuit experiment are used to demonstrate differentiation and integration by an RC circuit. Shown above are the circuits for differentiation (at left) and integration (at right). The photograph above shows a triangular wave (top trace) and its derivative, a square wave (bottom trace). Setting the capacitance at full scale (about 300 picofarads) and the resistance at half scale (about 50 kilohms), frequencies of 500 Hz for differentiation and 100 kHz for integration can be conveniently used.