Q&A

# Help with differential to single ended voltage converter

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Hello I don't understand how this differential to single-ended voltage converter can work.

What I don't understand is why we place a current mirror(a current mirror copies the current flowing through one transistor to another transistor) and how is the output voltage affected by the input voltages.

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First, let's draw the schematic properly so that it's not so annoying to look at:

Yes, it's a differential amplifier. Q1 sinks current as a function of VIN+. Q3 and Q4 are a current mirror that takes the current sunk by Q1 and dumps a current of the same magnitude onto Q2. When VIN- is a little below VIN+, that is more current than Q2 can sink, so VOUT goes high. When VIN- is a little above VIN+, then the current dumped onto Q2 is less than it will try to sink, so VOUT goes low. As a result, VOUT is the highly amplified difference of (VIN+ - VIN-).

One advantage of this topology is that the gain is very high. If the collector current of a BJT were truly independent of the collector voltage, then the gain would be infinite. This would be true even if the individual transistor gains were finite.

Another way to think about this is that Q4 is a current source driven by VIN+ and Q2 is a current sink driven by VIN-. When two ideal current sources are connected together like that, the result is either clipped high or clipped low whenever the two aren't exactly equal. The only reason VOUT will have any intermediate voltages is because the two current sources aren't ideal.

1. The loading on VIN- depends on VIN+. When Q2 is not saturated, R2 is reflected onto VIN- times the gain+1 of Q2. When Q2 is saturated, then the dynamic impedance seen at VIN- is only R2 directly.
2. The internal currents depend on the common mode voltage. This is usually undesirable when common mode rejection is important. The drive capability of VOUT is also proportional to the overall internal current level.
3. The low side of the VOUT range is limited by VIN-.

I have done some experiments on falstad and every time Vin+ becomes less than Vin- Q2 is driven to saturation and if Vin+ becomes more than Vin- Q4 is driven to saturation. Is that normal?

Yes, as should have been clear from the discussion above, particularly the third paragraph below the schematic: "the result is either clipped high or clipped low".

Quote:"When VIN- is a little below VIN+, that is more current than Q2 can sink, so VOUT goes high". Of course, I agree - however, what is the clear explanation? WHY goes Vout high? We have two (non-ideal) current sources with a conflicting behaviour. How and why does this fact influence the voltage at the common point?

This discussion is getting deeper and deeper into issues not originally asked. At some point, we have to assume basic electronics knowledge outside of what was specifically asked about. You can keep asking "why" questions indefinitely. "Why is grass green?" "Then why is chlorophil green?" "What makes it look green to us?" ...

However, I'll answer this one question this time. Consider the two current sources connected in series:

Both current sources are essentially controlled pass elements. They can't actively source current, only control how much current they let thru. For simplicity, let's also say their compliance range goes from 0 V to at least V+.

Now consider what happens when I1 is set to 2 mA and I2 to 1 mA. No matter how much current I1 tries to let pass, only 1 mA will flow because that's all that I2 allows. I1 will therefore turn its pass element fully on (act as a dead short). Vout therefore goes to V+. I2 is fine with that, and will continue to pass 1 mA.

The same applies the other way around when the current source values are flipped. If I2 is trying to let 2 mA pass, but I1 only allows 1 mA, I2 will turn its pass element fully on, and Vout goes to 0.

In the general case, Vout goes fully high whenever I1 is set to more current than I2. Vout goes fully low whenever I1 is set to less current that I2.

If you had two knobs that could adjust the values of I1 and I2, then the circuit becomes a comparator. Vout is V+ when I1 > I2. Vout is 0 when I1 < I2. I1 = I2 is a mathematical curiosity only, since no two signals are truly equal in the real world, and of course perfectly ideal current sources don't exist either.

The circuit works only for non-ideal current sources. There is no other way to solve the conflict with two current sources in series.

What I showed works fine for ideal current sources as long as they are passive. They can't supply any power on their own. They can only allow a certain current to pass, as noted.

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Question: What is the purpose of the current mirror?

Answer: It allows to combine the current changes in BOTH transistors (T1, T2).

Explanation In a classical differential amplifier (with separate collector resistances for T1 and T2) we must use the difference between the collector voltages or currents for further processing - when we want to use the full dynamic capabilities of the amplifier.

This can also be accomplished using the shown current mirror - with simultaneous double-ended into single-ended conversion.

Resulting from a differential input signal the collector currents of T1 and T2 change their values in the opposite direction. However, the current mirror does not "allow" such a change because it tries to keep the currents equal.

Therefore, the difference between the currents is available as an output current iout which drives the next stage, which makes the current-to-voltage conversion.

So we have:

ic1=ic3+2ib and ic2=-ic1=ic4+iout;

With ic4=ic3 this gives: iout=-2(ic1+ib)

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# My Comment

I will begin my answer by commenting on the other two answers from two months ago. I will show that they do not contradict but rather complement each other.

Ideal current sources. I can not agree with Olin Lathrop's assertion that this arrangement "works fine for ideal current sources as long as they are passive" since, as he himself has noted, the circuit will be a comparator and the output voltage will stay close to one of the supply rails.

Non-ideal current source(s). "To work fine" (to be linear) in the case of the open circuit (no load connected), at least one of the current sources must be non-ideal. So, the problem is how to make an ideal current source non-ideal. There are two ways proposed since the 19th century by Thevenin and Norton.

According to Thevenin. By its nature, an ideal current source consists of a voltage source and an infinite differential resistance in series. ("differential" means that it is infinite only for current changes). To make it non-ideal, we have to decrease its resistance (make it finite). In the transistor implementation of this idea (dynamic load), the resistance is decreased because of the Early effect.

According to Norton. But what do we do if we cannot change the internal resistance of the ideal current source? How do we make it non-ideal? Norton's idea can help us.

Intentional "worsening". For this purpose, we can connect a constant (ohmic) resistor in parallel to the ideal current source. It will divert a part of the current and the combination of the two elements will act as a real (non-ideal) current source.

Natural "worsening". In fact, as LvW has noted, such resistance always exists; it is the input resistance of the next stage.

So, this arrangement will work in both situations - Thevenin real current sources without load (open circuit) and ideal current sources with load.

Both explanations are correct but Olin's explanation will be true only in the case of real current sources while LvW's explanation will be valid in both cases (real and ideal current sources).

# My Explanation

We can see two clever ideas in this circuit solution that can be figuratively named dynamic load and transistor cloning. Let's try to explain them in an intuitive way.

LvW: "WHY goes Vout high? We have two (non-ideal) current sources with a conflicting behaviour. How and why does this fact influence the voltage at the common point?"

Current source. Exactly, LvW! This is the main question to be answered herе! Unfortunately, this cannot be done with the concept of current source and through this circuit of two current sources in series because it is not clear what is inside these current sources and how they function. The answer to this question can only be given through the concept of dynamic resistance. What is it?

Dynamic resistor. The two "current sources" in series actually are resistors… a special kind of resistors but still resistors. In contrast to ordinary ohmic resistors, their resistance does not stay constant but varies when the current tries to change. For example, if the voltage across such a dynamic resistor increases, it increases its resistance with the same rate of change and the ratio V/R = I stays constant. In addition, this property is controlled by an input voltage.

So, the full descriptive name of these elements (implemented by transistors here) can be "voltage-controlled current-stabilizing nonlinear resistors".

Voltage divider. Two resistors in series form the well-known 19th century voltage divider. If we keep the whole voltage across the network constant, and vary some of the resistances, the voltage drops across them will vary and we can take some of them (usually, the grounded one) as an output.

Potentiometer. If, in a variable voltage divider (the so-called potentiometer), both partial resistances r1 and r2 vary in opposite directions with the same rate, their sum will stay constant. As a result, the current I = V/(r1 + r2) is also constant; only the partial voltage drops across the resistances vary (crossfade) in opposite directions.

Dynamic voltage divider. Now imagine that there is some increasing gear on the wiper and it is enough to move it slightly and the voltage changes a lot. Here, this is a simple electrical analogy of our arrangement known as "dynamic load".

Dynamic load. So, the two transistors Q2 and Q4 act as voltage-controlled dynamic resistors that, under control of two oppositely (differentially) changing input voltages V- and V+, vigorously change their collector-emitter static resistances in opposite directions (they act as two crossfading dynamic resistances). As a result, their collector-emitter voltage drops vigorously redistribute (crossfade). The whole network acts as a kind of a super sensitive electronic potentiometer (high gain amplifier). Note (LvW) that no load is required for the circuit to operate in linear mode; it can operate on an open circuit.

CMOS stage is another excellent implementation of this idea.

## Transistor cloning

The network of two dynamic resistors is stretched between the supply rails so one of them is "pulling up" and the other is "pulling down". The voltage drop across the pull-down resistor is taken as a grounded output voltage.

The one input voltage VIN- is grounded and applied between the base of the pull-down "resistor" Q2 and ground. The problem is with the second input voltage VIN+ that is also grounded but, to control the pull-up "resistor" Q4, it should be applied between its base and Vcc… but this is impossible. That is why a clever trick is used which I call "transistor cloning".

VIN+ controls another grounded pull-down transistor Q1. Then, with the help of the current mirror, Q1 is cloned by Q4… as though, Q1 is moved above Q2.

From another viewpoint, the current mirror can be considered as an "electric transmission" that connects Q1 and Q2 to make the dynamic voltage divider.

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