08 - First Order Circuits

# 08 - First Order Circuits - EECS 215 First Order Circuits...

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EECS 215 First Order Circuits J. Phillips EECS 215 First Order Circuits A circuit with only resistors (and also Op Amps) results in algebraic expressions A circuit with energy storage elements results in differential equations dt v RC dv i o 1 = i f o v R R v 1 =

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J. Phillips EECS 215 First Order Circuits A first order circuit is characterized by a first order differential equation Resistors and capacitor only (RC circuits) Resistors and inductor only (RL circuits) Determine voltage/current as a function of time J. Phillips EECS 215 Source Free RC Circuit A “source free” circuit is where the DC source is suddenly disconnected ( ) 0 0 V v = At t=0, From KCL, 0 = + R v dt dv C 0 = + RC v dt dv ( ) RC t e V t v = 0 This is the natural response of the circuit, i.e. in absence of external sources
J. Phillips EECS 215 Math for the First-Order Differential Equation In this case, we can perform a simple integration ( ) A Ae V v RC = = = / 0 0 0 Differential Equation: 0 = + RC v dt dv ( ) RC t e V t v = 0 dt RC v dv 1 = = dt RC v dv 1 Integrate both sides: () K RC t v + = ln (K=unknown constant) Take exponent of both sides: K RC t e v + = / RC t Ae t v / ) ( = (A=unknown constant) Use initial condition to

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08 - First Order Circuits - EECS 215 First Order Circuits...

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