So, first year EE student, and I just learned about op-amps. I understand the ideal model, and know how to analyze them, and understand the idea behind them/the circuit that we were shown that is inside them. Except, that's not the real circuit, it has a dependent source. My question is, what is actually inside an op-amp? If we were to replace the dependent source with real sources, what would we see? (I guess this is also more of a question about 'What are dependent sources, really?'). I have searched everywhere, and I always find the same answer 'Dependent sources are useful tools to model a circuit'. But what are they really?
Here is a $35 kit you can make, which ends up being the equivalent of a 741 op-amp using discrete 13 2N3904 and 7 2N3906 transistors. It has eight binding posts representing the eight pins of the device.
Here is a link to the datasheet, which includes the schematic for the kit (shown below) and a BOM.
Compare that to a "real" 741 out of the TI datasheet:
They are virtually the same, even down to the resistor values.
"Dependent sources are useful tools to model a circuit'. But what are they really?"
Regarding "dependent sources": We discriminate between four different controllable (dependent) sources:
Voltage-controlled voltage source (VCVS), Current-controlled voltage source (CCVS), Voltage-controlled current source (VCCS) and current-controlled current source (CCCS).
Transistors (bipolar and FET): VCCS
Operational amplifier: VCVS
Operational transconductance amplifier (OTA): VCCS
Current conveyor (second generation, CCII): CCCS.
In reality, all dependent sources are non-ideal (finite input and output impedances, frequency-dependent). That means: Real dependent sources can be modelled using ideal dependent sources in conjunction with "parasitic" elements (resistors, capacitors)
Other answers have suggested looking at the implementation of real op-amps like a 741, but from a perspective of learning how they work, the best way to start is with a simplified system. The core of an op-amp is long-tailed pair. This can be built and operated or analysed in isolation to the rest of an op-amp, and provides the basic fundamentals of what an op-amp is. Looking at the 741 schematic, note that the transistor pairs (Q1,Q3) and (Q2,Q4) are substituting for the single transistors Q1 and Q2 in the diagram on wikipedia. The resistors in the wikipedia circuit are subsituted with transistors to allow the behaviour of that core amplifier to be optimized. The rest of the 741 circuitry is basically designed to improve on the response of this amplifier (removing offsets, increasing gain, improving frequency response, etc), and isn't strictly necessary to do the basic job.
Search for 'LM709 schematic', or 'LM 741 schematic'. Those were some of the first opamps available and have reasonably simple schematics. Modern opamps are based on similar principles, but generally have more complex circuits (because transistors are much cheaper now, and performance requirements keep increasing).
On the web sites of chip manufacturers you may find extensive documentation on most IC's, including the opamps that you actually use in your electronics lab. Such documentation often include the schematic diagram. Especially for opamp chips.