EE 315 Introduction to Electronic Analysis & Design
Lecture 11: Diodes I: A new circuit element, ideal diodes, first-glance analysis, rectifiers, gates, min/max circuits, super diodes, SPICE models

PN-junctions can be packaged to build diodes.

Diodes:

• Simplest (physically contstructed at least), fundamental, nonlinear circuit element note that I disagree with Sedra and Smith on this because signum functions or saturated op amps are probably simplier at least in their modeling
• Nonlinear circuit elements (doesn’t follow Ohm’s law as a line as the I-V relation)
• Act like voltage controlled valves
• Polarity matters
• Two terminals: anode (positive) and cathode (negative)
• Packaged in epoxy (plastic) or glass

Previous circuit elements were assumed to be linear (Ohmic)

• Resistors $v=iR$
• Capacitors (kind of like a frequency dependent resistor)
  • $Z_C = \frac{1}{j\omega C} = \frac{1}{sC}$
  • I-V related by calculus
  • $i_C(t) = C\frac{dv_C}{dt}$
  • $v_C(t)=v_C(t_a) + \frac{1}{C}\int_{t_a}^{t_b}i_C(\tau)d\tau$
• Inductors (kind of like a frequency dependent resistor)
  • $Z_L = j\omega L = sL$
  • I-V related by calculus
  • $v_L(t) = L\frac{di_L}{dt}$
  • $i_L(t)=i_L(t_a) + \frac{1}{L}\int_{t_a}^{t_b}v_L(\tau)d\tau$

Many important signal processing functions are not linear

• voltage dependent resistor (think of a resistor that changes as a function of the amplitude that is applied across the terminals)
• turing AC power supply voltage into a DC power supply rail
• waveform manipulation (amplitude demodulation, peak-finding, signum, etc.)
• digital logic and memory circuits (Schmitt trigger has memory/hyestersis for example)
• saturated op amps (nonlinear)
• importantly, no physical device is linear in reality and the diode is the first device where its nonlinearity is difficult to ignore in many instances

Comparing I-V curves.

Resistor		Diode
$i_R=\frac{v_R}{R}$		$i_D = I_S\bigg(e^{\frac{v_D}{V_T}}-1\bigg)$ (forward active region: $v_D > 0$)
		$i_D \approx -I_S$ (reverse biased region: $-v_Z < v_D < 0$)
		Voltage source (breakdown region: $-v_Z > v_D$)

Simplifying this behavior leads to the ideal diode model.

• Forward bias: positive voltage drop gives an approximate short circuit
• $v_D > 0V \implies R_D = 0 \Omega$
• Reverse bias: negative voltage drop gives an approximate open circuit
• $v_D < 0V \implies R_D = \infty \Omega$
• If a signal passes the break point of $v_D = 0V$, linear analysis is no longer permitted

Simple, first step to analyze circuits with diodes:

• Is the diode forward or reversed biased? Two approaches to figure it out.
• Approach 1: Take a KVL to see if $v_D > 0$
• Approach 2: Find $i_D$ and verify that it is entering the anode (positive terminal) of the diode

Positive logic systems

• Or gates
• And gates

Maximum and minimum input voltage circuits

• Select the voltage maximum as the output: create positive logic ‘or gate’ with various voltages (analog) at the input
  • Convince yourself by taking KVL around a loop with two input voltages
  • The diode in the path with the lower voltage will be reversed biased (off) that effectively disconnects the lower voltages from the circuit
• Select the voltage minimum as the output: create positive logic ‘and gate’ with various voltages (analog) at the input
  • Convince yourself by taking KVL around a loop with two input voltages
  • The diode in the path with the lower voltage will be forward biased (on) giving a short circuit to ground

Op amp based ‘superdiode’ circuit

SPICE model
.model myDiode D(Is=100pA n=1.679 BV=-10V IBV=-1mA)

Symbol	SPICE Name	Model Parameter	Units	Default
$I_S$	Is	Saturation current	Amps	1E-14
$r_S$	Rs	Ohmic resistance	$\Omega$	0
$n$	n	Emission coefficient		1
$V_{ZK}$	BV	Reverse-bias breakdown voltage	Volts	$\infty$
$I_{ZK}$	IBV	Reverse-bias breakdown current	Amps	1E-10