H1.1: DC networks
Introduction
Components and networks
- Passive: resistors, capacitors, inductors, diodes, …
- Active: capable of making signals larger / smaller, transistors, amplifiers, …
PCB: Printed Circuit Board
General
- PCB = connections are “printed” (actually etched) on a board (isolating
dielectric material), connections between different components are
printed on board
- All components are soldered to copper traces
Chip or integrated circuit
- Components integrated on 1 slice / 1 chip of semi-conductor material
- Chip is black part you see on PCB
- Wires connect chip with outside world
Chips and transistors
-
- At the bottom
- Modern transistor: 3 nm → on chip (1 cm x 1 cm)
IC design and CMOS
History of integrated circuits
- Moore’s law: more transistors on chip → make transistors smaller: bc of manufacturing cost
- Not possible on PCB bc there are so many transistors → a lot of connections → there is
always 1 that fails
Digital ICs and CMOS
- Complementary metal oxide semiconductor
o CMOS = nMOS + pMOS
o No DC current → perfect for digital
o Highest integration level & cheapest
Nanometer technologies
- Smaller transistors to increase integration level
1
,Voltage and current
Current
- Current = movement of charges (in a loop)
𝑑𝑞(𝑡)
- 𝑖(𝑡) = 𝑑𝑡
o Electric current tells us how much charge per unit time flows though area
o Symbol: I or i
o Units: A (Ampere) = Coulomb/time
-
-
o Current from a to b = iab
o Current from b to a = iba
o iab = -iba
Voltage
- Voltage = potential difference between 2 nodes, charge that is able of moving, similar to
potential energy
o Symbol: V or v
o Units V (Volt)
-
Power
- Power p = v*i
o Symbol: p or P
o Units: W (Watt)
- Voltage & current arrows are opposite → power calculated = power absorbed by
component, if negative → component is delivering power
- Voltage & current arrows in same direction → P = power generated by component, if
negative → component dissipates power
-
2
,Voltage source
- Battery, wall-plug adapter, USB charger, lab power supply
- Ideal voltage source
o Ideal: output voltage is independent of current through source
o Voltage is known but current
o Direction of Is chosen such that source delivers power but this is not necessary
o Note that voltage source can both generate & dissipate power
- Symbols: DC voltage sources
- Ideal, independent voltage source
o Regardless of current, Vs maintains value
o
▪ Is: current through component
▪ Vs: voltage across component
▪ We don’t know current, we only know
voltage
Current source
- Ideal current source
o Ideal: output current is independent of voltage across source
o Current is known but voltage depends on load network
o Direction of Vs chosen such that source delivers power
o Note that current sources can both generate & dissipate power
- Ideal, independent current source
o Regardless of Vs, Is maintains value
o
3
, Ohm’s law
Resistors and Ohm’s Law
- Resistor
o Linear relationship between current though resistor & voltage
across resistor
o Resistance of resistor; units: Ohm [Ω]
o Always dissipates power
- Resistor = component; resistance = property of component
- Ohm’s law: 𝑣𝑅 = 𝑅 ∗ 𝑖𝑅
Resistance and conductance
𝑖𝑅 = 𝐺 ∗ 𝑣𝑅
1
𝐺= 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑎𝑛𝑐𝑒 [𝑆] [℧] 𝑆𝑖𝑒𝑚𝑒𝑛𝑠
𝑅
Resistor: graphical representation
- 𝑣𝑅 = 𝑅 ∗ 𝑖𝑅
-
Resistor and physical parameters
- Resistivity of a material: 𝜌 [Ω𝑚]
𝑙
- 𝑅=𝜌
𝐴
-
Resistors and power
𝑝 = 𝑅 ∗ 𝑖²
𝑝=𝑣∗𝑖
⇒ 𝑣2
𝑣 =𝑅∗𝑖 𝑝=
𝑅
Voltage, current, resistance, power
4
Introduction
Components and networks
- Passive: resistors, capacitors, inductors, diodes, …
- Active: capable of making signals larger / smaller, transistors, amplifiers, …
PCB: Printed Circuit Board
General
- PCB = connections are “printed” (actually etched) on a board (isolating
dielectric material), connections between different components are
printed on board
- All components are soldered to copper traces
Chip or integrated circuit
- Components integrated on 1 slice / 1 chip of semi-conductor material
- Chip is black part you see on PCB
- Wires connect chip with outside world
Chips and transistors
-
- At the bottom
- Modern transistor: 3 nm → on chip (1 cm x 1 cm)
IC design and CMOS
History of integrated circuits
- Moore’s law: more transistors on chip → make transistors smaller: bc of manufacturing cost
- Not possible on PCB bc there are so many transistors → a lot of connections → there is
always 1 that fails
Digital ICs and CMOS
- Complementary metal oxide semiconductor
o CMOS = nMOS + pMOS
o No DC current → perfect for digital
o Highest integration level & cheapest
Nanometer technologies
- Smaller transistors to increase integration level
1
,Voltage and current
Current
- Current = movement of charges (in a loop)
𝑑𝑞(𝑡)
- 𝑖(𝑡) = 𝑑𝑡
o Electric current tells us how much charge per unit time flows though area
o Symbol: I or i
o Units: A (Ampere) = Coulomb/time
-
-
o Current from a to b = iab
o Current from b to a = iba
o iab = -iba
Voltage
- Voltage = potential difference between 2 nodes, charge that is able of moving, similar to
potential energy
o Symbol: V or v
o Units V (Volt)
-
Power
- Power p = v*i
o Symbol: p or P
o Units: W (Watt)
- Voltage & current arrows are opposite → power calculated = power absorbed by
component, if negative → component is delivering power
- Voltage & current arrows in same direction → P = power generated by component, if
negative → component dissipates power
-
2
,Voltage source
- Battery, wall-plug adapter, USB charger, lab power supply
- Ideal voltage source
o Ideal: output voltage is independent of current through source
o Voltage is known but current
o Direction of Is chosen such that source delivers power but this is not necessary
o Note that voltage source can both generate & dissipate power
- Symbols: DC voltage sources
- Ideal, independent voltage source
o Regardless of current, Vs maintains value
o
▪ Is: current through component
▪ Vs: voltage across component
▪ We don’t know current, we only know
voltage
Current source
- Ideal current source
o Ideal: output current is independent of voltage across source
o Current is known but voltage depends on load network
o Direction of Vs chosen such that source delivers power
o Note that current sources can both generate & dissipate power
- Ideal, independent current source
o Regardless of Vs, Is maintains value
o
3
, Ohm’s law
Resistors and Ohm’s Law
- Resistor
o Linear relationship between current though resistor & voltage
across resistor
o Resistance of resistor; units: Ohm [Ω]
o Always dissipates power
- Resistor = component; resistance = property of component
- Ohm’s law: 𝑣𝑅 = 𝑅 ∗ 𝑖𝑅
Resistance and conductance
𝑖𝑅 = 𝐺 ∗ 𝑣𝑅
1
𝐺= 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑎𝑛𝑐𝑒 [𝑆] [℧] 𝑆𝑖𝑒𝑚𝑒𝑛𝑠
𝑅
Resistor: graphical representation
- 𝑣𝑅 = 𝑅 ∗ 𝑖𝑅
-
Resistor and physical parameters
- Resistivity of a material: 𝜌 [Ω𝑚]
𝑙
- 𝑅=𝜌
𝐴
-
Resistors and power
𝑝 = 𝑅 ∗ 𝑖²
𝑝=𝑣∗𝑖
⇒ 𝑣2
𝑣 =𝑅∗𝑖 𝑝=
𝑅
Voltage, current, resistance, power
4
