1.8 Signal Representation

• Signals in the physical world are most commonly analog
• Value discretization forms the basis of the digital abstraction, which yields a number of advantages such as better noise immunity compared to an analog signal representation.

1.7 Modeling Physical Elements

• Resistor self-heating, with the associated change in value, prompts manufacturers to provide power ratings for resistors, to indicate maximum power dissipation (pmax) without significant value change or burnout.

• Battery terminal voltage expression: vt = V + iR

1.6 Ideal Two-Terminal Elements

• An ideal voltage source is a device that maintains a constant voltage at its terminals regardless of the amount of current drawn from those terminals.
• Two type of voltage source: independent & dependent
• An ideal conductor is a element in which any amount of current can flow without loss of voltage or power.
• An ideal linear resistor obeys Ohm's law
• Conductance (G) is the reciprocal resistance:

G = 1 / R

• The element law for a independent voltage source supplying a voltage V:

v = V

• The element law for ideal wire (short circuit):

v = 0

• The element law for open circuit:

i = 0

• The element law for a current source supply a current I:

i = I

1.5 Practical Two-Terminal Elements

• Power delivered by battery is the product of voltage and current : p = VI
• If a constant amount of power p is delivered over an interval T, the energy w supplied is : w = pT
• Ohm's law : v = iR
• An open circuit is an element through which no current flows, regardless of its terminal voltage
• A short circuit is an element across which no voltage can appear regardless of the current through it
• A two-terminal resistor is any two-terminal element that has an algebraic relation between its instantaneous terminal current and its instantaneous terminal voltage
• Associated Variables Convention define current to flow in at the device terminal assigned to be positive in voltage

1.4 Limitations of the lumped circuit abstraction

• Third postulate of lumped matter discipline requires signal speed to be significantly lower than the speed of electromagnetic waves
• Electromagnetic waves travel at 15 cm per nanosecond in insulator with 4x dielectric constant of vacuum
• Electromagnetic waves propagation delay across a 1-cm chip is about 1/15 ns
• When signal speeds are comparable to speed of electromagnetic waves, lumped matter discipline is violated, and therefore cannot use lumped circuit abstraction. ( resolve through distributed circuit model)
• Capacitive & inductive effects on lumped elements (resistors, wires) resulting from electric fields and magnetic fluxes generated by high frequency oscillator will violate lumped matter discipline ( resolve through separate these effects into new lumped element-capacitor & inductor)

1.3 The Lumped Matter Discipline

• Lumped matter discipline (constraints) provides the foundation for lumped circuit abstraction.
• Lumped matter discipline imposes three constraints on how we choose lumped circuit elements:

1. The rate of change of magnetic flux linked with any portion of the circuit must be zero at all time (allowed unique voltage across the terminals of an element)
2. The rate of change of the charge at any node in the circuit must be zero for all time. A node is any point in the circuit at which two or more element terminals are connected using wires. (allowed unique current across the terminals of an element)
3. The signal timescales must be much larger than the propagation delay of electromagnetic waves through the circuit

1.2 The Lumped Circuit Abstraction

• Capped a set of lumped elements that obey the lumped matter discipline using ideal wires to form an assembly that performs a specific function results in the Lumped Circuit Abstraction