To convert a digital number into an analog voltage, only a few resistors are needed. Many microcontrollers, in addition to PWM functionality, also have a DAC, which, unlike PWM, does not generate noise.
Today, we will look at a simple circuit that controls the brightness of an LED. It can be used in a dimmable lamp with a single button or a touch sensor and for creating light effects.
We’ll start with a frequency divider, also known as a counter. This will be needed to convert button presses or clock pulses into an increment of a binary number.
Counters and dividers are some of the most common building blocks in digital electronics. We are already familiar with many of them.
Remember the digital clock with no microcontroller? The crystal is factory-tuned to 32,768 hertz, i.e., oscillations per second.
This high frequency is chosen for two reasons. First, it is above the audible range. The quartz crystal vibrates inside the resonator case, and we don’t want the clock to produce any audible noise.
Second, the resonance frequency of a mechanical oscillating system directly depends on its size. This is why a bass guitar is longer than a regular electric guitar and has thicker strings.
12-inch speakers better convey the sound depth of an electric guitar. For jazz and heavy styles, guitarists often prefer them, sometimes even using giant 15-inch speakers.
On the other hand, some blues players prefer 10, 8, or even 6-inch speakers to emphasize mid and high frequencies. While some might argue that the same effect can be achieved with an equalizer, reproducing the mechanical resonance of a live guitar cabinet requires more than just EQ adjustments.
So, to make the clock crystal compact and inaudible, it was set to 32,768 Hz, which is 2^15. Divide the frequency by half 15 times, and you get one pulse per second.
This task in the digital clock circuit is handled by chip U11, a binary counter-divider CD4060.
But it only divides the crystal frequency Y1 fourteen times, so we needed another frequency divider using a synchronous D flip-flop U12A. The CD4013 chip contains two such flip-flops.
CD4518 is also a counter-divider, but it is a binary-decimal counter. It counts from 0000b = 0 to 1001b = 9, unlike a four-bit binary counter that counts up to 1111b = 15.
We typically use decimal digits rather than hexadecimal, so binary-decimal counters were designed to implement this format.
Decoders like CD4511 convert the code into digits on LED displays, allowing digital clocks to show time in a familiar format.
However, early tube computers did not have the luxury of seven-segment displays for graphical digits. Binary registers were viewed using neon bulbs: lit meant one, unlit meant zero.
Computers were created to speed up calculations. But for true performance gains, it’s necessary not only to compute quickly but also to input information and read the results fast.
Vintage calculating machines were great for this, as users, especially experienced accountants, could quickly read numbers written in standard decimal digits.
However, interpreting binary numbers as rows of bulbs was much more challenging and slower, as it required mentally converting binary code into decimal numbers.
You could use one bulb for each possible digit in each position. One of my favorite chips, the decimal counter-decoder CD4017, was designed for this purpose.
With it, you can create many interesting things, including a 2D LED matrix chaser light controller.
Today, tiny chips with tens, hundreds, or thousands of transistors inside cost only a few cents, and for a dollar, you can buy an entire pack of LEDs. What a great time we live in—a paradise for technical creativity!
A few decades ago, vacuum tubes were not only expensive and bulky but also required significant maintenance costs, starting with power consumption.
For tube computers, a cost-effective solution was needed for instant numeric display in registers that humans could easily interpret.
That’s when the abacus—a centuries-old counting tool widely used until cheap electronic calculators became common—was remembered.
In Japanese schools, lessons on using the Soroban abacus are still part of the curriculum because the Japanese value the high visual clarity of the abacus, which helps better understand arithmetic.
The abacus does not implement a purely decimal system but a bi-quinary system. This is almost like the decimal system, but with each ten split into two fives.
We can quickly perceive one to five objects or one lit bulb among five, unlike ten positions, which require more complex mental processing. This allows for very fast counting on the abacus.
Based on this, the IBM 650 and several subsequent computers implemented a bi-quinary system.
The 74LS90 counter, which we will use today, was designed specifically for this numbering system. It contains dividers for 5 and 2. By feeding the output of the divider by 2 into the input of the divider by 5, we get a standard binary-decimal counter.
Counter U3 is reset by pressing button SW3 and incremented by pulses on the CLOCK line. LEDs D3..D6 will display a binary-decimal number from 0000 to 1001, which will determine the voltage output at DACout.
To calculate these voltages, we need to understand the currents flowing through resistors R13-R18.
Our circuit is powered by 5 volts. At this voltage, the typical output voltage of the 74LS90 chip is 3.3 volts for a logical high and 0.2 volts for a logical low.
We can simplify calculations by approximating 0.2 volts to zero, but the 3.3 volts of the high level must be accounted for, as it’s significantly lower than the 5-volt power supply.
Resistor R17 is always connected to 5 volts, R18 is always connected to ground, and each of R13-R16 is either connected to ground or 3.3 volts, depending on the state of the corresponding output of the chip.
The voltage drop across the LEDs and their currents do not need to be considered, as they are directly connected to the outputs of the 74LS90.
The resulting voltage divider circuit is as follows:
The calculation of the divider with multiple resistors can be simplified by using units of conductance (G). One millisiemens equals 1 kilohm to the power of -1.
G = I/U
I = UG
The sum of incoming currents for our divider is (3.3V-Uout) (G17+Ghigh), and the outgoing currents are (Uout-0) (G18+Glow).
Let’s calculate the conductances of our resistors:
Gq3 = G13 = 1/10 kOhm = 100 uS
Gq2 = G14 = 1/20 kOhm = 50 uS
Gq1 = G15 = 1/36 kOhm = 28 uS
Gq0 = G16 = 1/82 kOhm = 12 uS
G17 = 1/6.8 kOhm = 147 uS
G18 = 1/2 kOhm = 500 uS
Thus, the voltage equation for the output of the resistive divider, expressed in millivolts is:
Gh(3300-Uout) = Gl*Uout
3300Gh - Gh*Uout = Gl*Uout
Uout = 3300Gh/(Gh+Gl)
Gh+Gl is the sum of all six resistor conductances:
Gh+Gl=12+28+50+100+147+500=837μS
Uout = 3300Gh/837 = 4Gh
With this simple formula, we can easily calculate the output voltages for each of the ten possible binary-decimal digits.
For 0000 Gh = G17 = 147 uS. Uout = 588 mV
For 0001 Gh = G17 + G16 = 147+12 = 159 uS. Uout = 636 mV
For 0010 Gh = G17 + G15 = 147+28 = 175 uS. Uout = 700 mV
For 0011 Gh = G17 + G15 + G16 = 147+12+28 = 187 uS. Uout = 748 mV
For 0100 Gh = G17 + G14 = 147+50 = 197 uS. Uout = 788 mV
For 0101 Gh = G17 + G14 + G16 = 197+12 = 209 uS. Uout = 836 mV
For 0110 Gh = G17 + G14 + G15 = 197+28 = 225 uS. Uout = 900 mV
For 0111 Gh = G17 + G14 + G15 + G16 = 197+28+12 = 237 uS. Uout = 948 mV
For 1000 Gh = G17 + G13 = 147+100 = 247 uS. Uout = 988 mV
For 1001 Gh = G17 + G13 + G16= 247+12 = 259 uS. Uout = 1036 mV
The output voltage from the resistive DAC goes to the operational amplifier U4A in a non-inverting configuration, then to a voltage follower U4B.
The gain of this amplifier is set by resistors R19 and R20 and equals 3. For a forward voltage drop of 1.7 volts on the green LED D7, the current through R21 and hence through the LED is:
Iled = 3Uout - 1700 uA
For 0000 Iled = 3*588 - 1700 = 64 uA
For 0001 Iled = 3*636 - 1700 = 208 uA
For 0010 Iled = 3*700 - 1700 = 400 uA
For 0011 Iled = 3*748 - 1700 = 544 uA
For 0100 Iled = 3*788 - 1700 = 664 uA
For 0101 Iled = 3*836 - 1700 = 808 uA
For 0110 Iled = 3*900 - 1700 = 1000 uA
For 0111 Iled = 3*948 - 1700 = 1144 uA
For 1000 Iled = 3*988 - 1700 = 1264 uA
For 1001 Iled = 3*1036 - 1700 = 1408 uA
The pulse generator for manual increment of the counter is a flip-flop composed of two NAND gates.
The remaining two NAND gates of the CD4011 chip form an automatic pulse generator for incrementing.
A monostable multivibrator on a 555 timer sets the operating duration for the astable generator on U2A and U2B. Note that the circuit has a flaw.
You either need to wire the inputs of U2A together or pull the anode of D2 to the power supply with a 10 kΩ resistor. Otherwise, with the input pin floating, the multivibrator on two logic gates is unstable.
If the DAC output voltage is fed to the brightness control input of a current source, it will provide a more advanced solution for an LED lamp.
