Lecture 4: Electrical Circuits• Electric circuits: resistors, capacitors, inductors, and OP-
Amp
• Basic laws governing electric circuits� Ohm’s Law
� Kirchhoff’s current law (KCL, node law): The sum of currents entering a node () is equal to the sum of currents leaving the same node () .
=
� Kirchhoff’s voltage law (KVL, loop law): The sum of voltage around any closed loop in an electrical circuit is zero.
1
Electrical Circuits• LRC circuit:
� Find mathematical equations� Find transfer function:
4
LRC circuit
• (• (
Electrical Circuits• Applying Kirchhoff’s voltage law
Taking the Laplace transform,
Transfer function
5
LRC circuit
Loop 1
Loop 2
Loop 1 Loop 2
• (• (
Complex Impedances• Transfer function
• Complex impedances� Resistance: � Capacitance: � Inductance:
Operational Amplifiers
• Op Amp is used to amplify signals.• Output• K: differential gain ()• No current flows into either input
of the op-amp (Input impedance is infinite)• Output impedance is zero
Operational Amplifiers• Obtain the transfer function • Since = =0
Hence • Transfer function
=
Inverting amplifier
Filters
Low pass filter High pass filter
Impedance of capacitor decreases as frequency increases.
1𝑅𝐶𝑠+1
𝑅𝐶𝑆𝑅𝐶𝑠+1
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