How do Digital and Analog Clocks Work?

0:00 Inside almost every piece of technology is a tiny clock

0:03 that ticks at a rate of over a billion times a second,

0:07 generating a digital heartbeat that is

0:10 critical to regulating the execution of code,

0:13 the movement of data in the processor and memory,

0:16 the generation of wireless signals for transmitting data and much more.

0:20 So then, how do we generate a clock

0:24 that precisely pulses at less than half a nanosecond?

0:28 It might seem counter-intuitive,

0:30 but this billions-of-times-a-second heartbeat, or gigahertz clock signal,

0:35 is incredibly similar to how a ten-dollar

0:39 analog wall clock ticks through the seconds, minutes, and hours of the day.

0:44 In order to explore how a gigahertz technological heartbeat is generated,

0:49 let’s open a wall clock, see how it works,

0:52 and then see how the same technology is

0:54 used to produce your desktop computer’s gigahertz clock signal.

1:03 So, let’s jump right in.

1:10 Inside this ten-dollar wall clock are 5 unique systems that enable it to work.

1:16 The most recognizable is the gear train made from 8 gears.

1:20 At the beginning of the gear train, a driver gear is rotated by an electromagnet

1:26 which provides the force to rotate the clock hands.

1:30 This electromagnet is composed of a coil of wire,

1:33 which uses electrical current to generate a magnetic field,

1:37 and a strip of iron to channel that magnetic field to the drive gear.

1:43 Every second the electromagnet switches directions,

1:46 thus causing the magnet inside the driver gear to rotate 180 degrees

1:51 in order to align its permanent magnet

1:54 with the fields produced by the electromagnet.

1:58 Therefore, the driver gear rotates fully around once every two seconds.

2:03 Most of the gears in the gear train are composed of compound gears,

2:08 each of which has two different gears, one on top of the other.

2:12 To move the second hand, which is mounted on a shaft through the clock center,

2:17 we go through a 12 to 48 gear reduction and then an 8 to 60 gear reduction,

2:24 thereby reducing one revolution every 2 seconds down to one every 60 seconds.

2:30 The minute hand is also mounted on a shaft through the center

2:35 and is driven through an 8 to 64 gear reduction to the idler,

2:39 followed by 8 to 60 to the minute hand.

2:42 And finally, the hour hand is driven via a 15 to 45 reduction to the idler

2:49 and a 10 to 40 gear reduction to produce one rotation every 12 hours.

2:55 As a result, we have 3 shafts rotating

2:58 to which the hands of the clock are mounted, each rotating at different speeds.

3:04 The last gear is used to set the time,

3:08 and interestingly this gear has 13 teeth on it,

3:12 and rotates once every 69 minutes.

3:15 As in the name, the time-setting gear

3:18 directly rotates the minute and hour hands, however,

3:22 the gear with the second hand doesn’t move

3:24 because the two parts of this compound gear slip

3:27 from the high torque required to rotate the second

3:31 hand 52 times per rotation of the time-setting gear.

3:35 Now that we’ve covered the gear train,

3:38 let’s dive into the quartz crystal oscillator and see what makes

3:42 this clock nearly identical to the digital clock in your computer.

3:46 Inside this metal cylinder is a quartz

3:49 crystal tuning fork with wires printed onto

3:52 the side which travel along the legs to the outside of the metal canister.

3:57 Let’s focus on a single side with wires printed on the left and right.

4:03 Inside the quartz is a crystal lattice of one silicon

4:07 for every two oxygen atoms which forms a network of covalent bonds,

4:12 with electrons being more attracted

4:14 to the oxygen due to their electronegativity.

4:16 When you cut a slice of quartz in a particular direction,

4:20 you can see repeating sections of a crystal

4:23 lattice with a hexagonal organization of oxygen and silicon.

4:27 When a negative charge is applied to the printed wires,

4:32 an electric field is directed to the crystal lattice

4:35 and the negatively charged oxygen atoms are pushed away,

4:39 whereas the positively charged silicon is pulled towards the wire.

4:44 The combined movement of all the oxygen moving away and the silicon

4:48 moving towards the wire results in a lengthening of the crystal lattice.

4:53 Conversely, when a positive charge is applied,

4:56 oxygen moves towards the positive charge and the silicon away,

5:01 and as a result, the crystal lattice shrinks in length.

5:05 This lengthening and shrinking along the length of the crystal lattice,

5:09 called the piezoelectric effect,

5:11 causes the leg of this tuning fork to move back and forth.

5:14 Let’s move back to view the tuning fork

5:16 crystal with wires printed on each of the sides.

5:17 As mentioned before, when a voltage is applied,

5:19 the tuning fork lengthens and bends outwards and when the voltage is turned off,

5:24 the quartz bounces backward.

5:26 The crystal bounces back and forth creating positive

5:29 and negative voltages with the frequency of oscillation being dependent

5:33 on the orientation of the crystal lattice as well

5:37 as the shape and dimension of the cut crystal.

5:40 The purpose of having two legs is to create a vibrational mode

5:44 wherein the prongs vibrate and resonate together while the base doesn’t move.

5:49 Frequently manufacturers add small amounts of metal to the ends

5:54 of the crystal to tune it to the desired frequency.

5:58 However, to get a crystal to continuously oscillate,

6:01 a changing voltage needs to be repeatedly applied to the wires on the legs.

6:06 Specifically, this voltage needs to match the movement

6:10 of the crystal such that the peak

6:13 positive voltage is aligned with the movement of the crystal in one direction,

6:17 and the opposite when the crystal moves in the other direction,

6:21 kind of like pushing a kid on a swing set when it’s at its low point,

6:26 but in both directions.

6:27 To do that we use an integrated circuit with an inverter to form a feedback loop

6:33 and two capacitors to assist in the timing

6:35 of the voltage from the inverter and feedback loop,

6:39 thus producing a resonant movement in the crystal.

6:42 This is a rather complicated circuit to fully explain,

6:45 but here’s one way of thinking about it.

6:48 An inverter on its own flips the input from a 1

6:53 to an output of a 0 and vice versa.

6:57 However, if we loop an inverter back in on itself,

7:00 depending on the physical design of the inverter,

7:03 the output will continuously flip between one and zero,

7:07 a few picoseconds per cycle.

7:09 And, if we add the crystal tuning fork

7:13 and capacitors in the path of the feedback loop,

7:16 then the flipping between 1 and 0 and back

7:20 is regulated by the geometry and movement of the prongs

7:23 of the crystal oscillator tuning fork and the filling

7:27 and emptying of the charges in both of the capacitors.

7:30 For this wall clock, the time it takes is 30.52 microseconds

7:36 per cycle resulting in 32,768 cycles per second.

7:42 The signal is then fed to another section

7:45 in the integrated circuit where a binary counter counts each cycle,

7:49 and after 32,768 cycles, which takes one second,

7:54 a signal is sent to the electromagnet controller

7:58 telling it to flip the direction of the electromagnet,

8:02 thereby rotating the driver gear around 180 degrees and moving

8:06 the hands of the clock forward by one second.

8:10 One thing to note is that if your clock is either fast or slow,

8:15 it’s most likely because the crystal

8:17 oscillator doesn’t oscillate exactly at 32.768

8:20 kilohertz due to the geometry and incorrect resonant frequency of tines.

8:26 These crystals typically have 20 parts per million accuracies,

8:31 meaning it can gain or lose at most 1.7 seconds a day,

8:37 or 10 and a half minutes a year.

8:40 As mentioned earlier, this wall clock is composed of a set of systems

8:45 with each falling under a different domain of science and engineering.

8:50 These topics are rather complex and typically covered by college courses,

8:55 but instead of paying thousands of dollars there’s a free

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9:25 For example, in a single afternoon, you can learn about gear trains,

9:30 then dive into oscillations and classical mechanics followed

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10:38 Let’s move on and see how smartphones and computers

10:42 generate a clock between 1 to 5 gigahertz

10:45 which is 30 to 150 thousand times faster than

10:49 a single oscillation of this quartz crystal tuning fork.

10:53 Let’s look again at this inverter looped back upon

10:56 itself and add two more inverters into the loop,

11:00 thus creating a ring oscillator.

11:02 Due to the odd number of inverters,

11:05 the output rapidly oscillates between a 1 and a 0.

11:09 These inverters can operate incredibly quickly and can

11:13 easily reach the gigahertz frequency range and higher.

11:18 However, the issue is that this ring oscillator’s frequency is highly

11:22 dependent on temperature as well as the physical geometry and electrical

11:27 properties of the transistors and thus has a frequency range

11:31 of plus or minus 50 percent or more from the desired frequency.

11:37 Therefore, to stabilize the output frequency of a ring oscillator to less than

11:41 a few parts per million accuracy we use a circuit called a phase-locked loop.

11:46 This is a complicated circuit, but here’s the general idea of how it works.

11:52 On the right, we have the ring oscillator,

11:54 and when we add some additional circuitry, depending on the input voltage,

12:00 the output frequency changes,

12:02 and the ring oscillator is now called a voltage-controlled oscillator or VCO.

12:07 On the left we have a 16-megahertz crystal

12:10 oscillator similar to the tuning fork crystal oscillator,

12:14 but by changing the crystals’ geometry

12:16 and placing electrodes on the top and bottom,

12:19 we get a crystal with a faster resonant frequency.

12:22 And again, this crystal is placed in a feedback

12:26 loop of its own to produce a stable resonant frequency.

12:30 In the middle is a frequency and phase comparator that outputs

12:34 a signal equal to the difference

12:37 between the crystal and the voltage-controlled oscillator.

12:39 Next, an integrator takes the output from the phase comparator and turns it

12:45 into a steady voltage and uses

12:48 it to drive the voltage-controlled ring oscillator.

12:51 Finally, this frequency is fed back into the frequency

12:55 and phase comparator, and as it is,

12:58 the feedback loop will drive the ring oscillator to match

13:01 and be identical to the output from the 16-megahertz crystal oscillator loop.

13:06 However, since we want to get, for example, a 2.4 gigahertz signal,

13:12 which is 150 times that of the 16-megahertz crystal oscillator,

13:18 we add a frequency divider into the feedback loop.

13:21 This frequency divider is just like the one in the wall clock

13:26 that took 32,768 cycles per second and turned it into a 1 hertz signal,

13:32 rather now, we’re dividing by 150.

13:35 Next, the signal is sent to the frequency and phase

13:39 comparator which wants the two signals to be identical.

13:44 However, by having them different,

13:46 it outputs a signal which goes through the integrator,

13:49 turning it into a steady voltage,

13:52 and driving the voltage-controlled oscillator up to a higher frequency,

13:56 which will be exactly 150 times that of the 16-megahertz crystal,

14:02 which is 2.4 gigahertz.

14:04 Using this phase-locked loop we have

14:07 an incredibly fast frequency generator producing a signal

14:11 that is exactly 150 times

14:14 that of a reliably manufactured and temperature-stable quartz crystal.

14:18 Additionally, if we want to change the desired frequency,

14:22 we have the binary counter divide by a different number,

14:26 thus changing the amount the 16 megahertz crystal is multiplied by.

14:30 And in fact, all smartphones do this when not actively in use

14:36 in order to the reduce clock frequency

14:39 of their processor and conserve battery life.

14:42 That’s pretty much it for clocks and crystal oscillators.

14:45 One thing to note is that sometimes MEMS oscillators are

14:49 used in smartphones to save space instead of crystal oscillators,

14:54 and we’ll dive into MEMS in a future episode.

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