Why is analog electronics so complicated?

Computers and digital technology have taken over everything for a reason. Today, even the simplest analog device, like a timer, the developer would prefer to make on a microcontroller, instead of using a 555 chip.

There are reasons for that.

1. Digital is very scalable and repeatable. You don't need to know the internals of a circuit or a library. You use it as a building block to build something of your own. This works both in the processor architecture and in high-level code.

2. Digital is linear and predictable due to the absence of continuous processes. It is like a precise mechanism – if you set it up, it will not go wrong. Computers are often called machines because they are essentially mechanisms. Only electronic ones.

Of course, there are errors in digital too, but they often occur at such high frequencies that analog begins to interfere with the digital.

The analog is nonlinear. And this is exactly what I will show in the simplest circuit examples below.

The analogue is not scalable. This follows from nonlinearity. A small change in the essential characteristics of the module often requires a radical change in the circuit, components and even operating principles.

Every analog circuit requires tuning. Like a guitar string, it can go out of tune over time. It can also be temperature sensitive, have hysteresis, and bring many other surprises.

Today I will show you with simple examples where linearity begins and ends in analog. I really wish someone had told me this at university, but I had to figure it out on my own.

Basics

Analog electronics starts with Ohm's law And law of continuity of flow. Let's take the simplest circuit: a resistor R clamped between the supply V and ground.

The difference in levels between the supply and ground causes electrons to flow from V to ground. Resistance tries to slow down the rate of this flow. The result is a current of I = V/R. This is Ohm's law.

And here everything is linear. The more power, the more current. The more resistance, the less current. If we replace R with a potentiometer, we get a linear change in current.

For a second it may even seem that nature is kind to us. There are no exponents or polynomials here.

Let's add another (current-limiting) resistance in series and I will show the law of conservation of flux.

1. Since the current has nowhere to go, it flows in equal quantities through R1 and R2. Let's denote the total current as I

2. Such a connection of resistances is no different from one equivalent total resistance. Ohm proved this fact experimentally, and not this “obvious, understandable” of yours.

3. According to Ohm's law, the current flowing is equal to the voltage divided by the resistance R1 + R2. Okay, we found the current. In this system, the only thing we don't know is the voltage Vx. Let's find that too.

4. Let's write Ohm's law for the potential difference between Vx and ground. We know the current, we know the resistance. Let's find Vx. It turns out to be proportional to the supply voltage V, proportional to the resistance R2 and inversely proportional to the total resistance.

I think you know what this scheme is called voltage divider. And it outputs a part of the input supply voltage to its output. We can control this circuit using the parameter R2, if we replace it with a potentiometer.

The dependence turned out to be nonlinear. By changing the control resistance, we also change the total resistance. But such nonlinearity is not bad. It changes smoothly from zero to the maximum supply voltage.

This nonlinearity can be easily overcome by using one potentiometer and taking readings from its midpoint. Thus, the total resistance is always constant, and the control one can smoothly change within its limits.

But this is where linearity in analog electronics ends.

Let's add some load

So far the voltage divider we have designed exists on its own. To use it, we need to attach its output to some circuit so that it can do something useful.

I would like to write about lighting an abstract light bulb, but people will immediately rush to the comments with the current-voltage characteristics of real LEDs, and I don’t need that. Therefore, we will simply drive the current through the load resistance. Let’s see how this little surprise will quickly break everything for us.

1. An additional path is created for the current from Vout to the ground wire. The sum of the currents I2 and I3 is equal to the current through R1.

2. Vout is currently unknown, but we want to find it. To do this, we write Ohm's law three times: for the potential difference V-Vout through R1, we find the current I1

3. For the difference Vout-0 through R2 and for the difference Vout-0 through r we find the currents I2 and I3 respectively

4. Through the equality of currents we get an equation in which only Vout is unknown. Consider that we have found the solution. But its presence does not make it any easier.

In my humble opinion, this is the most important formula of analog electronics. Looking at it, everyone should decide for themselves whether they want to continue with analog or choose something else.

To understand how the output of such a divider will behave, let's measure R2 in fractions of the load resistance r, look at the type of formula and compare it with the formula of a divider without a load.

1. By connecting two resistances in parallel, we create an additional path for the current between the potentials. The equivalent resistance is described by a nonlinear formula.

2. This causes a skew in the circuit. The control knob, now the alpha parameter, no longer allows the output voltage to change linearly.

3. What's worse is that as the resistance of the knob increases, when a >> 1 (much greater than one), the current starts to leak more and more towards the load, and now r is our divider, not the knob at all. We completely lose control over the circuit.

What are some ways to fix the situation?
It would be logical to use a load with a relatively high resistance so that our handle never goes beyond the permissible resistance limits. But in this case, a tiny current will leak into the load.

Amplifier

In analog electronics, all parts of the circuit are a single, inseparable whole. They influence each other, like a load on a voltage divider. The only way to separate the parts of the circuit from each other is with a large (ideally infinite) resistance. But the weak input current must then be amplified somehow.

At this point, you should already understand why the Nobel Prize was awarded for the invention of the transistor. The transistor perfectly solves the problem of multiplying a small input current by a given coefficient. Before that, they used bulky lamps that broke and heated up a lot, and the transistor was also compact.

Transistor circuits are also some kind of thing, better than nothing, but the mass user wants an even simpler and more linear solution.

That's why the operational amplifier appeared. A kind of linear multiplier without the side effects that a transistor has. If you look at any professional circuit, almost everything will be surrounded by operational amplifiers to reliably isolate the modules from each other.

Выводы

But we have considered only the simplest static schemes. When some dynamics need to be organized in an analog (to generate a signal, for example), complex exhibits come with it, which allow signals to penetrate into the most remote corners of the schemes, as well as derivatives. The systems of equations from linear become linear differential.

It is incredibly difficult for us to understand. And the people who invented all this? Heroes! All analog electronics are the result of sorting through a huge number of hypotheses by many people, some of which turned out to be working.

If this were not so, then each amplifier would not bear the name of its inventor. Some Gauss of the 20th century would simply come along and invent all possible transistor amplifier circuits.

Overall, I hope it was interesting. Thank you all for your attention!