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Interconnecting 5v and 3.3v logic

Direct connection

5v to 3.3v

A logic input may be described as "5v tolerant" meaning that even when powered by a lower supply voltage the device will not be harmed by driving its input to 5v. In that case a 5v output may be connected to a 3.3v input.

3.3v to 5v

A logic input may be described as "TTL compatible", meaning that it has a lowered input threshold, typically 2.0v. This means that a 3.3v powered CMOS device can reliably drive the 5v input high. In that case a 3.3v output may be connected to a 5v input.

3.3v to a 5v rated LCD module

This special case comes up again and again, due to the abundance of cheap 5v alphanumeric LCD modules. There are two fairly easy options

1: Operate the LCD from 5v, and rely on the display recognising 3.3v as logic high. The HD44780U and ST7046 both give a VIH of 2.2V so this is acceptable. This is best reserved for "write-only" designs as reading the LCD would put 5v on some of the data pins, though on LPC microcontrollers the pins are 5v tolerant anyway.

2: Operate the LCD from 3.3v and supply a negative contrast voltage. Use your favourite charge-pump circuit or "nick" the bias from a RS232 driver as the current is tiny. Add a series pot if needed and that should give sufficient contrast. You could even configure a microcontroller PWM output to supply the "pump" waveform. Below-zero voltages for contrast ARE allowed, and some display types require a negative bias anyway even for 5v operation. 3.3v operation of a 5v LCD will slow down the internal clock by roughly 25% so software delay times may need lengthening.

Interconnected tristate outputs

My advice is to translate to a common logic level before combining outputs on a bus.

Warning: Tristate outputs are frequently NOT over-voltage tolerant. The upper FET typically has a parasitic diode that will become forward-biased if the output is driven higher than the supply. Some devices avoid this problem by isolating the substrate of the upper output FET when in tri-state.
Even if devices are tolerant beware of contention between a 3.3v and 5v device outputting simultaneously.
One place this can be an issue is a SPI bus with multiple devices on different voltages. An alternative strategy might be to add pull-up resistors then combine the outputs with a logic AND gate instead of commoning them!
Before I knew better I once designed a circuit with a tristate buffer with a diode in series with its positive supply to prevent backflow. This worked suprisingly well, but meant that the buffer was powered from a supply about 0.6v too low.

Buffered connection (Parts suitable for plugblock, DIP or equivalent)

Note: I'm assuming one of the motivations for using MBED is plugblock development, and that a list of SMT-only devices would not be very helpfull.

Multiple lines, 3.3v to 5v, Available in DIP

For this I would recomend any "74HCT" series part, powered by the destination supply (5v).

Multiple lines, 5v to 3.3v, Available in DIP

For this I would consider the 74HC4050 (or 74HC4049) which are notable for having voltage-tolerant inputs, powered by the destination supply (3.3v).
The 74AHC... series have voltage-tolerant inputs and Texas Instruments parts should be available in DIP packages.

Buffered connection (Adapted to DIP)

Buffered connection (Surface mount)

Single lines

For single lines I would advise looking at SOT23-5 or SOT323-5 style "Tiny" logic, powered by the destination supply.

MC74VHC1GT125 This part looks very usefull as a level translation bridge. The supply range is 3.0v to 5.5v meaning the output can be made compatible with either supply voltage, and the input is both 5v tolerant and "TTL compatible" e.g. it will accept 3.3v logic levels. Remember that "equivalents" do not always have the same voltage tolerance, some parts are limited to 3.3v maximum or have an input protection diode that conducts if the input exceeds the supply.

Multiple lines, mixed function

SN74LVCC3245A 8 translators, with a direction pin and a tristate pin. Note that side B is always the 5v side.
TXB0108PWR is bidirectional and auto-sensing for lines WITHOUT pull-up resistors, note it tends to pull a logic line to whatever its current state is, so it will prevent a line from "floating" when it is not actively driven. Not recommended for I2C, but it is a good candidate for SPI systems as it will handle the single-data-line bidirectional variant. A module is available from Adafruit with 0.1" pitch pads. Relatively expensive.
TXS0108EPWR is bidirectional and auto-sensing for logic lines that have pull-up resistors. As it is auto-sensing the signal directions may be mixed. It should support I2C. Its a relatively expensive option though, and may lead to raised power consumption if used for logic signals that idle low. I have not seen a module available with this device, however the TXB and TXS devices appear to have a common pin-out so it might be possible to change the chip on the Adafruit module.
With both the TXB and TXS parts the A side is the lower voltage side and has the OE pin so the A side typically connects to a microcontroller, also the B side appears to have better ESD protection.

Problems with incorrect level translation

Be aware that a design that works in prototype may prove unreliable in production.

At low speed or DC conditions a typical 5v HCMOS gate will transition at very near 2.5v, and a 3.3v device will output almost 3.3v, allowing the 3.3v circuit to drive 5v CMOS parts marginally so an undemanding sub 1MHz application would be expected to work.
At raised speeds the HCMOS gate may need an input of 4v (80% of Vdd) in order to meet its performance specification and the 3.3v device may only reliably output 3.0v (limited by risetime). At best this will lead to significant pulse-shortening or stretching, at worst signals may not get through at all.
At speeds above 10MHz a 5v CMOS signal driving a 3.3v-compliant input may lead to noticeable pulse stretching, even though the input requirements have been met.
When a production design depends on a logic device's specific voltage tolerance characteristics it is important to remember that generic devices with the same function code may not have the same characteristics, meaning that common substitutions may cause problems. As an example looking at single buffers in SOT23 package all I checked had overvoltage tolerant inputs but only some had tolerant outputs.

5v to 3.3v issues

Raised power consumption if current flows from the 5v section to the 3.3v section. Note that although this leakage would be expected to source current to the 3.3v ssection it is possible that parasitic-transistor effects may cause current drain from the 3.3v supply as well. This may also lead to noticable heating of the device.
Abnormal operation due to 3.3v section being pulled up to a higher voltage. This may cause the 3.3v section to output a higher than normal logic level, meaning that other 3.3v to 5v translation issues appear when the pull-up problem is fixed.
Abnormal operation of analog functions due to current flowing into pin. This may manifest itself as huge errors in ADC readings, for relatively low currents. NOTE I do not know if the MBED shows this, it probably doesn't due to the pin voltage tolerance. The effect was quite noticable on some other microcontrollers.
Latch up damage. This is the bogeyman of mixed voltage circuits, and thankfully modern logic is very resistant. Latchup occurs because a CMOS device contains a PNPN structure as a side effect of its construction, and this behaves like a very hard to trigger thyristor. A device in latchup will present a near short circuit across its supply rails, and may be destroyed if current is insufficiently limited. If current is limited the device will recover once the supply voltage collapses, meaning that a serious latchup event may be mistaken for a software crash. Fortunately modern parts may require hundreds of mA before latchup is a real threat, so even as little as a 10 ohms series resistance may provide protection.

3.3v to 5v issues

This is generally the safer case, since the reduced voltage is unlikely to cause damage.

Raised power consumption may occur due to input not being driven properly high and causing CMOS cross-conduction.
Ambiguous logic levels lead to slow low-to-high transitions, this can make a clock waveform very assymetric.
Ambiguous logic levels may fail to register as logic high in extreme cases.

Separate supplies, same voltage

This is a special case of level translation, where two supplies have the same voltage but are different in some way. An example would be digital and analog supplies sourced from different regulators, or just a module-to-module interconnection. Translation is not required but problems may occur if the supplies come up at different times, or if one suffers a short circuit. The CD4050 and 74HC4050 parts should be considered. As a bare minimum current should be limited by series resistors or by using known "weak" outputs.

Translating other voltages: 12v logic (4000 series CMOS)

It should be possible to translate SPI to 12v and use a 12v shift register to obtain a large number of 12v "ports". This may be a viable alternative to a 3.3v register and 8 or more parallel translators.

12v to low level

74HC4050 has 15v tolerant inputs
CD4007UBE can be used to make two downward level shifters (among other things). Unusually for CMOS it brings the source terminals of the FETs out on individual pins so it is possible to construct a gate with a lower output range than its supply rails. It is also notable in that on 4 of the 6 FETs the source terminals are separated from the substrate.

low level to 12v

CD4504 has a 5v to 15v translation function and the inputs may be put into "TTL mode" to enable compatibility with 3.3v logic.
ULN2803 octal open collector driver
MIC5821 has eight outputs but has a shift register and several MIC5821 devices may be daisy-chained and controlled by one SPI port. Watch the clock speed though.

low level to 12 volt BIDIRECTIONAL

A N-type MOSFET could be used in "common gate" mode with the gate connected to the logic supply or slightly more positive, the source connected to the low-level logic and the drain connected to the 12 volt circuit. Pull-up resistors will probably be needed on both sides. If the drain is pulled to ground externally then the source will be pulled down initially by the body diode and then by drain to source conduction due to the gate voltage biasing it on. If the source is driven to ground then the FET will conduct normally.

Other voltages: Bipolar

Bipolar supplies may be usefull to allow a positive-only ADC or DAC to be used with balanced supplies such as +/- 2.5v. It is also sometimes desirable to operate 24v relays from a system's +/-12v rails to minimise current, though this approach originated in systems with symetrical linear supplies e.g. +/-12V, and is unsuited to modern switching power supplies that have a far greater current available from the positive supply compared to the negative.

74HC4053 analog switch has a Vee pin which accepts a negative supply below the logic "ground" level though watch out for the 10V limit
RS232 line driver e.g. MC1488
RS232 line reciever e.g. MC1489 (Note that the recommended supply is 5v)
I have seen quad comparators used as relay drivers. One input was biased to the logic threshold and the device ground was connected to -12v. 24V relays were used

Special cases

I2C bus level translation

MANY hardware implementations should be 5v-tolerant, but
Frequently a microcontroller implementation may be restricted to 3.3v, particularly if the I2C pins are multi-function and not dedicated
Good results have been obtained with the two-FET translator method in 3.3v systems (with lower voltages its harder to find a compatible FET), however please be aware that this method does NOT change the logic threshold of the low-voltage part (because the FET turns on for logic-low, bypassing it) nor does it buffer or regenerate the signal.
Unfortunately for plugblock experimenters most IC solutions appear to be in very small SMT forms not DIP
Some I2C translator ICs are really just implementations of the two FET method, though they may add active pull-up drive to increase speed.
True I2C buffers exist, these will improve noise immunity and signal range. Pay attention to datasheets though, because of the bidirectional nature of I2C these devices may use various "tricks" to determine signal direction, for example on the microcontroller side the buffer may only pull down to a specific voltage not ground. The voltage will be low enough to register as a logic low on the micro, but not low enough to activate the buffer's line driver.
For those looking for an all DIP IC solution, for example for plugblock or stripboard designs, it may be worth looking at the CD4007UBE instead of discrete pass transistors. Biased from 5V the N-channel FETs would only pull up to 2V on the part I tried, but would pull down sufficiently to work with a 4.7k pull-up. As these are effectively 4-terminal FETS if the gate was taken to 0v the device would isolate completely. Drawbacks would be a relatively high on-resistance and a complete dependence on passive pull-up.

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A "Plugblock compatible" I2C translator. Due to the FETs having grounded substrate it doesn't matter which side is the higher voltage side, and with no parasitic diode it can be disabled to isolate the busses.