Voltage-Basic Electronics-Lecture 01-Electronic and Information Engineering, Lecture notes of Basic Electronics

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Prof. C.K. Tse: Basic Circuit

EIE209 Basic Electronics

Basic circuit analysis

Prof. C.K. Tse: Basic Circuit Fundamental quantities ® Voltage — potential difference bet. 2 points

® “across” quantity

® analogous to ‘pressure’ between two points

® Current — flow of charge through a material

® “through” quantity

® analogous to fluid flowing along a pipe

Prof. C.K. Tse: Basic Circuit Power and energy Work done in moving a charge dq from A to B having a potential difference of V is W = V dq

Power is work done per unit time, i.e.,

A

B

dq

Prof. C.K. Tse: Basic Circuit Direction and polarity n Current direction indicates the direction of flow of positive charge n Voltage polarity indicates the relative potential between 2 points: + assigned to a higher potential point; and – assigned to a lower potential point.

n NOTE: Direction and polarity are arbitrarily assigned on circuit

diagrams. Actual direction and polarity will be governed by the

sign of the value.

Prof. C.K. Tse: Basic Circuit Dependent sources n Dependent sources — values depend on some other variables

Prof. C.K. Tse: Basic Circuit Circuit n Collection of devices such as sources and resistors in which terminals are connected together by conducting wires. n These wires converge in NODES n The devices are called BRANCHES of the circuit Circuit Analysis Problem: To find all currents and voltages in the branches of the circuit when the intensities of the sources are known.

Prof. C.K. Tse: Basic Circuit

Overview of analysis

n Ad hoc methods (not general) n Series/parallel reduction n Ladder circuit n Voltage/current division n Star-delta conversion n More general n Mesh and nodal methods n Completely general n Loop and cutset approach (requires graph theory) Done in Basic Electronics!

NEW

Prof. C.K. Tse: Basic Circuit Series/parallel reduction n Series circuit— each node is incident to just two branches of the circuit KVL gives

Hence, the equivalent resistance is:

Prof. C.K. Tse: Basic Circuit Note on algebra n For algebraic brevity and simplicity: n For series circuits, R is preferably used. n For parallel circuits, G is preferably used. For example, if we use R for the parallel circuit, we get the equivalent resistance as which is more complex than the formula in terms of G:

G = G

1

+ G

2

+ … + G

n

Prof. C.K. Tse: Basic Circuit Ladder circuit n We can find the resistance looking into the terminals 0 and 1, by apply the series/ parallel reduction successively.

First, lumping everything beyond node 2 as G 2 , we have

Then, we focus on this G 2 , which is just G 20 in parallel

with another subcircuit, i.e., We continue to focus on the remaining subcircuit. Eventually we get

Prof. C.K. Tse: Basic Circuit Example (something that can be done with series/parallel reduction) Consider this circuit, which is created deliberately so that you can solve it using series/parallel reduction technique. Find V 2. Solution: Resistance seen by the voltage source is Hence, Current division gives: Then, using V 2 = I 4 R 4 , we get

Prof. C.K. Tse: Basic Circuit Oops! Series/parallel reduction fails for this bridge circuit! Is there some ad hoc solution?

Prof. C.K. Tse: Basic Circuit Star-to-delta conversion For the Y circuit, we consider summing up all currents into the centre node: I 1 + I 2 + I 3 =0, where

Y (star) D^ (delta)

Thus, , and

Prof. C.K. Tse: Basic Circuit Star-to-delta conversion

For the D circuit, we have

Y (star) D^ (delta)