This is the basic trick question. This circuit will not work - and you should be able to say why? In my "apprenticeship years" (45 years ago) above said problem nicely bothered me :-)
Maybe I did not express full exactly. In that case, I apologize. Of course, the issue is that there must be "DC Way" also to the non-inverting input. The mentioned situation is quite clear. The situation is less clear if the capacitor is "hidden" in the signal source - and it's not obvious at first sight.
To solve the problem, we have to add the proper resistance from the non-inverting input to ground - this will substantially change the input resistance of the structure.
Another problem with op-amps is using the gain product bandwidth deliberately as a first order low-pass filter. Doesn't always give the expected result.
Yes, I like the bootstrap. On the 'high' frequencies behaves like an infinite resistance (ideally) and at low frequencies as inductor in series with resistance. See for example
We even can exploit the pole(s) of an opamp for realizing "R-oscillators".
And there is another story about ideal vs. real opamps: There is a well-known oscillator structure that will oscillate for real opamps ONLY. It will not oscillate if "everything" is ideal. Funny.
If the amplifier is ideal, does not "produce" a frequency dependent phase changes, thus it is "not able to oscillate". Then we must use the traditional good feedback circuits :-) Their properties determine required - not by adverse variance parameters of amplifiers. In practice, it is advisable to work where the amplifier is somehow perfect.
If you allow me, I will go back to the initial essential point and will supplement it with a few more questions.
IMO it is interesting to see why these "10 mega ohm biasing resistances" (Simone) are not internally implemented. Are they really "biasing"? If so, how they bias the op-amp?
MOhms are difficult to implement in silicon. Though today some microcontrollers have the resistor (or an equivalent) 'on board'.
Regarding the resistor it cannot bias, but taking into account the parasitic input capacitance (single-digit pF) you get an RC constant in the multi-µs range - effectively biasing the input at around VCC/2.
"MOhms" can be implemented as constant-current elements (transistors)... but nevertheless it is not accepted to integrate them internally. Why?
Strictly speaking, the alone resistor cannot bias; the voltage source connected in series with this resistor is that which can bias. But where is this voltage source here?
Your question is excellent but there is a need of a reasonable explanation of the role of the input "biasing" resistors connected between the op-ap inputs and ground (or other appropriate point). My opinion is that they are not biasing resistors; if they were such, they would determine the bias current... but they don't...
Frankly, I expected more... Well, obviously I myself have to write what I want to read:)
As you have shown in your nice pictures, the transistors of the op-amp input differential stage are biased from the side of the emitters by inserting there a bias current source. It injects the bias current directly into the common emitters of the two transistors forming the long-tailed pair. Thus the emitter current source forces the transistors to adjust their base-emitter voltages, accordingly their base currents, so that to pass the half emitter currents through their collector-emitter junctions (a cascode configuration). In this way, both bases remain vacant for the input signals and the "soft" emitter current source allows the emitters to follow the (common-mode) base variations. I have considered this mechanism in detail below:
Now at crux of the matter... Note that this biasing from the side of the emitters is prepared in advance but it comes into play only when we somehow close the paths of the base bias currents from the side of the bases. For this purpose, we have to connect some "jumpers" between the bases and ground (or other "stiff" point)... and in no case we should leave the inputs unconnected because the op-amp will saturate.
Ideally, galvanic input voltage sources act as such "natural jumpers". The problem is when capacitors are inserted in the input circuit (your case study). Then we need to close the path of the biasing current by additional "artificial jumpers" (resistors)... and this brings new problems...
To control the transistor from the side of the emitter, the base voltage should be fixed (common-base configuration). But if the "jumper" has relatively high resistance, the base will "move" when the emitter source tries to "move" the emitter. As though, in this case, the base resistor acts as a kind of a "base regeneration"?
Let's finally see where bias currents flow. Accoding to Cyril's Golden Rules about currents:))), every current returns to where it has started... and should be presented by a fully closed path (loop). Look at the attached picture (from a similar question) to see where bias base currents flow (pay no mind to the input source VIN).
As you can see, the bias current (e.g., IB1) "departs" from the positive terminal of the negative power supply V-... enters into the right ground... leaves the left ground... passes through the "jumper" RB1... base-emitter junction BE1... emitter "current source" (the humble resistor RE here but you can imagine a perfect current source instead)... and finally, successfully returns to where it has started - the negative terminal of the negative power supply V-. So, the bias base current is created only by the negative power supply.
I would comment that "real world" op-amps are vastly more complex even in their equivalent datasheet schematic representations, whereas Josef's is a simplified minimal circuit to demonstrate basics of the situation (and yes could hold true if being built out of discrete components, for example in a power amplifier input stage).
The bottom line is that ac coupling an op-amp's non-inverting input without a resistive reference to some fixed point is going to end in tears.
I prefer current source simply (in collector) - not dynamic load. It enables to sever value of "collector resistance" and quiescent current (thus supply voltage, too). Ideal curent source has infinity output resistance - and we can use small supply voltages. This idea enables to construct modern OPAs. Certain problem is DC quiescent voltage of the T1. But in "full structure" all solves negativ feedback (DC).
Well, strictly speaking, the upper part of your circuit ("current source") is exactly a dynamic load since it changes its static (chordal) resistance when the lower part tries to change the common current. But, as a whole, this is not a pure dynamic load arrangement because of the parallel negative feedback introduced by RB.
IMO it is not correct to set the quiescent current from the side of the collector; it is more correct to set it from the side of the emitter as it is usually done in the long-tailed pair. But this is another story... here it is not possible...
Yes, this is the case (cascode configuration) where "a current source sets the quiescent current from the side of the emitter"... The problem is only that the emitter is "movable" (due to the 100% serial negative feedback) and there is no gain. This problem is successfully solved in the differential pair where another transistor (emitter follower) keeps the emitter "immovable":
But I can agree that if we introduce a 100% parallel negative feedback in the first configuration (RB = 0, e.g., by connecting the collector to the base), they both become the same cascode configuration where two dual electrical sources interact - a current source (T2) sets the current through a voltage source (T1)... and v.v., a voltage source (T1) sets the voltage across a current source (T2)...
In the first circuit diagram above I see a common-emitter stage (T1) drawing a current from a common-base stage (T3)... and this composed stage is comprised by a parallel negative feedback (through RB)... and it is driven by the upper current source (T1).
Usually, such a cascode (T1 + T3) is used to prevent from the Early effect...
In the second picture, the network R1-R2 is bootstrapped... and thus acts as a dynamic load (current "source").
The output is boosted by T2 (emitter follower).
So, the common basic idea in all these circuit solutions is to set the quescient current by a current source included in the collector? And, in order to "soften" the conflict between the two current "sources", a parallel negative feedback is applied?
Hi Cyril, in these simple situations is negative feedback from the collector the simplest solution. For AC signals we are easily able remove the feedback. See below.
Sophisticated solutions created with a lot of imagination and fantasy...
As I can see, in regard to the AC signals, the final circuit solution is already a real dynamic load arrangement where two current "sources" connected in series "fight" each other... As a result, the voltage of the middle point between them vigorously changes (high gain).