# Digital

## Useful equations to remember

###### Power consumption

${P}_{T}={V}_{cc}{I}_{l}+{V}_{cc}^{2}f\left({C}_{pd}+{C}_{L}\right)$$P_T=V_{cc}I_l+V_{cc}^2f(C_{pd}+C_{L})$

${V}_{A}={V}_{ref}\frac{{t}_{2}}{{t}_{1}}$$V_A=V_{ref}\frac{t_2}{t_1}$

### Verilog

• Remember that for any MOS the last operand is the gate

## Diode Logic

• Can only make And/or gates
• Large signal degredation when cascaded
• Not must be made using active transistor

## TTL

### Series

Denoter Speciality
74 Basic TTL
74H High Speed
74LS Low power Schottky
74L(Obselete) Low Power
74S(Obselete) Schottky
74F Fast

### Block Diagram

• a phase splitter simply outputs the signal and an inverted version

### Logic Gates

The phase splitter and output stages are always the same, only the logic changes between modules.

## CMOS

• NMOS - makes a good 0
• PMOS - makes a good 1
This is due to the gate reference voltage aka if a pmos was pulled to ground the device would turn off having to turn on a bit to make the ground better in turn making the output higher than desired.

## Inverter

### Nand

each new input is simply a new emitter on the transistor

### Fan In

• Fan in is the number of inputs a logic gate has (generally limited by on resistance)
• Fan in can also be increased by cascading gates

### Fan Out

• This is the number of gates that can be driven from the output of one without strain
• Calcumated by the max output current divided by the input current (must be calculated for high and low and the minimum taken)

### Noise Margin

• Generally noise margin is given as a function of supply voltage
• Noise margin is calculated on the high side by the difference between minimum input and minimum output and opposite for low noise margin.#

### Power consumption

Total power consumption is the addition of static and dynamic power losses

### Static Power Consumption

• power lost by leakage current
$V=IR$$V=IR$

### Dynamic Power Consumption

• Power lost by partial short circuits during capacitor discharge (P_T)
• Power lost by charging external capacitances(P_L)

### Design Notes

• Keep unused pins of logic gates tied to vcc or ground
• Use “Decoupling capacitors” to supply a peak of power when switching the output to avoid supply noise/strain
• For drving resistive loads just act logically

### Open Drain

Open drain devices are devices where the drain is unconnected and so the designer must choose the resistor and supply themselves.
This also means the PMOS section of the circuit is removed
Useful for Driving LEDs
Useful in Multisouce busses

### Multisource bus

Multiple devices connected to a single output. Only one output can be on at once hence each gate has an enable to put its data onto the bus.
When all enables are low the output is pulled high.
Nand gates are used and so the data value on the bus is the inversion of the data that is on the enabled gate

### Tristate output

Tristate circuits have 3 states they exist in: High, Low, Disconnected(high impedance). The enable pin when high allows signals to flow but otherwise acts as an open switch not allowing any current to flow.

### CMOS Tristate Buffer

Here if the enable is set to low then both the transistors are off rather than the usual one one one off state

### CMOS Transmission Gates

Multiple transmission gates can be used for XOR, XNOR and multiplexers.

## Analogue to Digital

Remember nyquist theorem (sampling frequency must be at least twice the maximum frequency to avoid ailiasing)
The more bits the largers the resolution of the device but more storage and processing needed.
The signal is first passed through an anti-aliasing filter. This filter then is sampled and stored and fed into the ADC (Analogue to digital convertor).

When the ADC is working the input must be kept constant so the sample and hold circuit must hold one anlogue value constant for the sampling time.

### Holding/Sampling

Here the input is buffered and charges a capacitor to the input value the swich is then turned off and the capacitor acts like a constant voltage output with a buffer attached giving a stair step like response out of the holder.

The vref and resistor network acts as a group of reference potential dividers.These are compared to the voltage in and in turn turn their outputs on depending on what the voltage is like a bobber in a water tank, this is then encoded into binary using a priority encoder on each enable pulse.
Flash converters are hardware expensive but fast.

WHen a Vin is applied and a clock produced initially the msb is set high, this is then converted to analog and compared to vin, if the comparator outputs a high then keep this value on otherwise set the bit to 0. keep cycling this moving down in bit significance untill at the lsb where the aproximation is complete and the binary can be output.This method is slower but much less resource heavy (requiring the number of bits as clock cycles to make an aproximation).
Note the S/H stands for a sample hold as previously seen.

this method is used a lot in measurment methods.

Here an inpit voltage VA charges an integrator creating a ramp function for anmount of time, this ramp is then discharged by a reference voltage

the time taken to discharge to 0V is then measured and the output voltage given by

## Digital to Analogue convertors

### Binary Weighted DAC

and by thevenin/norton each bit of magnitude n equates to

### Settling time

Settling time is the amount of time the output takes to never oscillate above the magnitude of the least significant bit.

## Memory Heirachy

The higher up the tree the more the memory costs but the faster it is.

## Principal of Locality

### Temportal Locality

If a memory location has been accessed recently it will be likely accessed again soon

### Spatial Locality

If a memory location has been accessed the next to be accessed is likely nearby

### Memory cache

Takes advantage of temporal and spatial locality by keeping recent and nearby code in a fast access memory location.(On-chip and off-chip SRAM)

### SRAM Cell

The bitlines set or read the value and the wordline enables the data on the bitlines.
Data is lost when the power is turned off

##### Write

To write to SRAM the bitlines are set to the values desired and then the wordline is enabled to put this data onto the cell.

To read the data both bitline and bitline’ are set to 1 and then the word line enabled, a sense amplifier then measures current flow to detect if there was a 0 on the bitline or bitline’

### DRAM cell

charge leaks over time and must be refreshed
Data is lost when the power is turned off

##### Write

To write to a DRAM cell the data is set on the bitline and the word line set high to charge or discharge the capactior accordingly. the wordline is then turned off keeping the capacitor charged.

To read the bitline is set to neither high nor low but inbetween and the word line turned on, a sense amplifier then detects if current was sourced or sunk which is recovered as a 1 or a 0.

Denoter Speciality
DRAM slow asynchronus
SDRAM Synchronous DRAM
SDR SDRAM Single data rate (one word per clock cycle)
DDR SDRAM Double data rate (two words per clock cycle)
DDR4 Lots of weird things

### Dual Port Ram

Can read two bits in one cycle
Can only write one per cycle as both channels are required#

### Flash

Here the gate is forced to high or low voltages by applying voltages to the source, drain and gate. Due to its oxide surrounding leaves the charge floating. When a positive is applied to the control the floating gate becomes negative and is associated with a binary 0. Otherwise a negative on the gate causes a positive on the floating gate equating a binary 1.

## External memory interfacing

### System Bus model

Here the control buss differentiates between addressing memory or I/O

Here a control pin is used to differentiate between whether data or address is on the bus. This reduces pins but can slow datarate

### Memory Mapped I/O

A memory map simply splits up available addresses saying what can be found in each section (generally the program starts at 0)

#### Isolated I/O

Different busses are used for I/O lines than for memory

#### Memory Mapped I/O

The bus is shared for I/O and memory where the I/O is memory mapped after the memory.

### Asynchronous Data transfer

#### Destination initated transfer

Here a request is sent for the data and after the data access time (ta) the data appears on the bus to be read. The data after the minimum hold time is then taken off the bus (unless not requested to)

#### Source initiated transfer

Here the source puts the data on the bus and then sends a control signal to say the data is ready to be read. The data is then read and data ready goes low then removing the data on the bus.

### Handshaking

Both destination and source initiated transfer are known as strobing and works well for deterministic devices. If the data is unpredictable such as on the internet a protocal called handshaking must be used.
Here the data is sent the same way with data bus and data ready pulses but also the reciever returns data acknowleged to the source to let it know it has been read.

This is where an external processor takes information from I/O directly to memory instead of via the processor, this frees us processor time.

A data transfer signal is sent to the controller and in turn the controller sends a hold interrupt to the processor where the CPU disconects from the busses and thus giving control to the controller to directly put data in the memory. The hold signal is then low and the CPU gains control of the busses again.

# Semiconductors

## Useful equations to remember

$np={n}_{i}^{2}$$np=n_i^2$
$J=\sigma E$$J=\sigma E$
$V=\mu E$$V=\mu E$
$F=eV$$F=eV$

###### conductivity equation

$\sigma =nq{\mu }_{e}+pq{\mu }_{h}=q\left(n{\mu }_{e}+p{\mu }_{h}\right)$$\sigma=nq\mu_e+pq\mu_h=q(n\mu_e+p\mu_h)$ (for intrinsic $\sigma ={n}_{i}q\left({\mu }_{e}+{\mu }_{h}\right)$$\sigma=n_iq(\mu_e+\mu_h)$)

###### Diode equation

$I={I}_{0}\left({e}^{\frac{eV}{kT}}-1\right)$$I=I_0(e^{\frac{eV}{kT}}-1)$

###### Fermi Dirac

$P\left(E\right)=\frac{1}{1+{e}^{\frac{E-{E}_{F}}{KT}}}$$P(E)=\frac{1}{1+e^{\frac{E-E_F}{KT}}}$

###### Wave equations

$E=hf$$E=hf$
$f=\frac{c}{\lambda }$$f=\frac{c}{\lambda}$

###### Charge neutrality

$n+{N}_{a}=p+{N}_{d}$$n+N_a=p+N_d$

# Analogue

## Useful equations to remember

${g}_{m}=\frac{{I}_{c}}{{V}_{be}}=\frac{e{I}_{c}}{KT}$$g_m=\frac{I_c}{V_{be}}=\frac{e I_c}{KT}$
$\beta =\frac{{I}_{c}}{{I}_{b}}$$\beta=\frac{I_c}{I_b}$
$\tau =\frac{1}{{\omega }_{0}}$$\tau=\frac{1}{\omega_0}$

###### Op-Amp open loop gain equation

${A}_{V}=\frac{{A}_{0}}{1++j\frac{f}{{f}_{0}}}$$A_V=\frac{A_0}{1++j\frac{f}{f_0}}$

###### First Order Low Pass Standard form

$\frac{{V}_{o}}{{V}_{i}}=k\frac{1}{1+j\frac{f}{{f}_{0}}}$$\frac{V_o}{V_i}=k\frac{1}{1+j\frac{f}{f_0}}$