If a transistor is a solid state digital switch, how can it also function as an analog amplifier?

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If a transistor is a solid state digital switch, how can it also function as an analog amplifier?

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A digital switch does not mean that it can’t also let a controlled current through, the behavior depends on the control sitgnal.

Compare it to a water walve. If you only have it fully open or fully closed it is like a digital switch. But you can only just open it a bit and control the water flow,

When transistors are used for digital logic the control signal you use are the min or max voltage so it is fully open or fully closed. But as an analog amplifier, you have it in the middle range then it is partially open.

So what you consider the transistor as will depend on how you use it.

You can look at a digital switch as an amplifier with very high amplification and a large input signal. Above half the max voltage is increase the voltage and below half the max voltage it decreases the voltage. It can only amplify it to max voltage and decrease it to zero volt

Add to that a signal with voltages up to max voltage and down to zero voltage and you will the majority of the time overdrive it and the output is just maxed or min.

Bot the amplification and input signal lever is inappropriate for an analog amplifier where you like a higher voltage variant of the input signal. There has to be a balance between input signal voltage, amplification and max output voltage to avoid you overdriving the amplifiers. A digital switch are a deliberate design so the vast majority of the time you overdrive it

If you look at how a transistor in digital circuits works in reality the voltage does not imitate change from min to max. It rises from min to max and during that time the transistor is partially open or partially closed. In digital logic when you try to do stuff as fast as possible the clock frequency is so high that this is a very relevant effect.

Just consider them a switch and you have a signal that just is at max and min is an idealization. The analog properties of the switch can often be very important.

Digital signals do not really exist. They are always analog in reality and change at a limited speed, there is also noise in them.

Here is a for example oscilloscope image of the signal in an ethernet cable

https://upload.wikimedia.org/wikipedia/commons/7/77/Oscilloscope_screenshot_of_Ethernet_transmission.jpg

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