ECE 1270: Introduction to Electric Circuits Lecture 6: Advanced Nodal Analysis Chapter 4 Techniques of Circuit Analysis: Sections 4.3,4.4

Dependent Sources and Their Applications ____ Controlled Voltage Source ____ Controlled Voltage Source ____ Controlled Current Source ____ Controlled Current Source Example: Voltage Amplifier Example: Transimpedance Amplifier Example: MOSFET Switch Example: Bipolar Junction Transistor

Node Voltage Method: Dependent Sources Find unknown voltages by summing the currents leaving each node Example 4.3 Step1: Label Nodes Step2: Define Node Voltages

Node Voltage Method: Independent Sources Step3: Write Current Leaving Each Branch Passive Sign Convention Substitute iϕ with Step4: Solve Simultaneous Equations in Standard Form Find the unknown voltage or current

AP4.3a: Find power associated with each source Simultaneous Equations: Passive Sign Convention Solution p50V= p5A= p3 i1=

Super Node

Supernode Circuit with voltage source between two nodes Combine nodes to form a supernode

Fig. 4.13: Voltage Source Between Nodes Step1: Label Nodes Step2: Define Node Voltages

Fig. 4.13: Voltage Source Between Nodes Step3: Write Current Leaving Each Branch At Node 2 Passive Sign Convention At Node 3 Now add them together (or isolate i and equate them) to get Eq.1: Step4: Solve Simultaneous Equations in Standard Form What about Eq. 2?

Alternative: Create a Supernode - Now we can write Eq.1 directly as … - What about Eq. 2?

AP4.5 (create super node): Find v Passive Sign Convention Simultaneous Equations: Students do this example Solution v=

Passive Sign Convention AP4.6: Find v1 Passive Sign Convention Simultaneous Equations: Solution v1=

Passive Sign Convention AP4.4: Find vo Passive Sign Convention Simultaneous Equations: Students do this example, Help set it up first Solution vo=

Example: Transistor Circuit* *=if time permits Note: When a signal level is low, it can be passed through an amplifier to increase its level. An amplifier can be built from BJT transistor. The following schematic represents a part of the amplifier. See page 98-99 for equations Find Vo if Vcc=15 V, R1=100 kΩ, R2=50 kΩ, Rc=10 kΩ, RE=4.25 kΩ, β=300