Circuit Response

Thursday, 23 August 2018

12:34 PM

The response of a circuit is the way it reacts to an excitation

Natural response -> Behaviour of the circuit (in terms of voltage or current) due to the initial energy stored and physical characteristics

 

Forced response -> Behaviour of the circuit (in terms of voltage or current) due to external sources and excitation

 

 

 

Natural Response

Machine generated alternative text: Natural response of RC circuit Let's consider a circuit with a single capacitor, charged to an initial voltage Vo and connected to a resistor. How will it behave? c We can use KCL to get: dv v -c dt Note: We will consider how this capacitor was charged later in this lecture. Note: A circuit characterised by a first order differential equation is called a first order circuit.

 

Machine generated alternative text: Solve differential equation: Rearrange: Separate: Integrate: v(t) = erc+D Solve for v(t) v(t) = AeÄT Apply initial conditions v(t) = VoeÄT -c dv 1 — dv = In(v) — —1 dt RC —t

 

Machine generated alternative text: • There is no need to derive the differential equation solution every time, just use the result. • The result shows that the voltage response of the RC circuit is an exponential decay of the initial voltage. v(t) = Voe-ÄÜ

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Machine generated alternative text: Natural response of RC circuit • Follow these steps to find the natural (or source-free response) of RC circuits: 1. 2. 3. 4. Find the initial voltage v(O) = Vo across the capacitor before it is connected to the resistor. — The capacitor is assumed to be fully charged at the beginning and can be replaced with an open circuit. Find the time constant T = RC. If the circuit has more than one resistor, the resistance that we need to find in order to calculate the time constant is the equivalent resistance as seen by the terminals of the capacitor, i.e. the Thevenin equivalent resistance R = RTh. When possible, this resistance can be obtained by simplification of series or parallel resistances. Calculate the voltage across the capacitor as v(t) = Voe¯F. Find any other circuit variable using the capacitor's voltage. Note: A switch which opens or closes can remove part of the circuit or add something to it.

 

 

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