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Math Functions: Logarithmic Circuits

 Circuit Takes Square Root of Input Voltage: 11/20/97 EDN-Design Ideas Commutating Amp Performs Log Function: 02/16/95 EDN-Design Ideas Log amp uses capacitor charging law: 01/10/2002  EDN - Design Ideas / The novel logarithmic amplifier in Figure 1 relies on the exponential charging characteristics of a simple RC circuit. The expression for the time, T, required for a capacitor, C, to reach a voltage (VIN-VK) from 0V, when charged through a resistor, R, with an applied voltage of VIN, is VIN-VK=VIN (1-e-T/RC), where VK is a fixed voltage. . Logarithmic Amplifier: Logarithmic amplifier uses the log caracteristic of PN (diode, transistor) to implement logarithmic function. The second transistor is used as refference and with the PTK resistor minimizes the dT/dV coeficient. Model Fixed Point DSP Arithmetic in C: 03/18/99 EDN-Design Ideas / PDF contains multiple circuits - scroll to find this circuit Primer on Binary Arithmetic Rounding: 01/21/99 EDN-Design Ideas / PDF contains multiple circuits - scroll to find this circuit Reference stabilizes exponential current: 10/25/2001 EDN - Design Ideas / In an antilog converter, the difference between the base voltages of two transistors sets the ratio of their collector currents: The use of matched transistors balances the first-order temperature coefficient but leaves a temperature-dependent gain term, q/kT. Classic antilog circuits use a thermistor in the drive circuitry to correct this temperature dependency. . Software Filter Boosts Signal Measurement Stability, Precision: 02/03/03 Electronic Design - Ideas for Design / Small or embedded systems often require a delicate measurement in the presence of high noise or interference. Without fancy filtering hardware, high-speed processing, or digital signal processing, it can be difficult to extract a stable signal of... Square Root Function Improves Thermostat: 09/30/99 EDN-Design Ideas / Perhaps the most elementary rule of control-loop design theory is that feedback-loop performance is fundamentally linked to the careful choice—and stability—of loop gain. Insufficient loop gain leads to poor setpoint accuracy. Too much gain can induce feedback instabilities, such as overshoot, ringing, and, ultimately, oscillation. Therefore, the greater the accuracy you expect from a control system, the more critical maintaining near-optimal loop gain becomes.