Question about the operation of a current mirror

[Master1022]

TL;DR Summary

How does a current mirror work?

Hi,

I am in the process of trying to understand how a current mirror (shown in the diagram below) works. At a high level, I understand that we are trying to replicate the reference current ($V_{cc}/R_x$) at the output. However, I am slightly confused as to how the current actually is created there; I don't understand the logical steps which make the load current equal to the input current.

- The reference current splits off and feeds into the two bases of the transistors
- The base currents activate the transistor and allow the same level of collector current to pass through both transistors.
Where does that load current come from?
It seems like the base current of the transistors have set the capacity - and thus both collector currents are able limited by the same value so we can equate them by just saturating the input. However, I am not sure where that load current comes from?

Otherwise, maybe I have misunderstood the circuit and the point of this mirror is the replicate the reference current to the load current, but the load current is the final leg of a circuit (rather than acting as a current source feeding into a circuit)?

I do apologize for the confusion. I have been through the mathematical derivation to prove that the load current equals the reference current, but am not sure about the physical explanation.

Any help is greatly appreciated.

 

[DaveE]

The load current comes from it's connection to the power supply. It is determined not by where it comes from, but by how much the transistor will allow to flow. The transistor will determine the voltage across the load by changing the voltage at it's collector in response to how many electrons are allowed to flow to the collector.

The key point here is that the two transistors are matched. They share the same base-emitter voltage, which determines the base current and thus the collector current.

All of this assumes that the devices are operating in their linear region; i.e. neither all the way on (saturated) or all the way off (cutoff).

I suppose if you really want to understand this you could substitute the Ebers-Moll model of a transistor and solve the circuit. But I think it's conceptually easier to just rely on the fact that matched transistors do the same thing, and are relatively insensitive to the collector voltage within the linear region.

There are lots of online descriptions of how current mirrors work. Have you tried searching for them?

 

[LvW]

Summary:: How does a current mirror work?
...
- The reference current splits off and feeds into the two bases of the transistors
- The base currents activate the transistor and allow the same level of collector current to pass through both transistors.
Where does that load current come from?
It seems like the base current of the transistors have set the capacity - and thus both collector currents are able limited by the same value so we can equate them by just saturating the input.

I think, the confusion on your side results from a fundamental misunderstanding of the transistor function. The working principle of such a simple current mirror can be understood only if you realize that the collector currents are determined by the voltage Vbe only (and NOT by the base current).
The BJT works as a voltage controlled current source Ic=Is[exp(Vbe/Vt)-1].
From this equation the transconductance is gm=d(Ic)/d(Vbe)=Ic/Vt.

Hence, any change in Vbe will result in a corresponding Ic variation. As you can see from the diagram: Both base nodes are connected and, hence, both voltages Vbe are forced to be equal. Therefore, the collector currents will be equal.
Please note that I did not even mention the base currents. In this context, you should realize that both base currents are very different (the most left one works close to saturation !); they do not play a decisive role.

 

[Master1022]

Thank you very much @DaveE and @LvW for your replies!

Yes, you are correct that I misunderstood and confused the role of the base current and base-emitter voltage. I did try to watch some videos and read explanations on the internet, but I didn't find any satisfactory explanations.

The load current comes from it's connection to the power supply. It is determined not by where it comes from, but by how much the transistor will allow to flow. The transistor will determine the voltage across the load by changing the voltage at it's collector in response to how many electrons are allowed to flow to the collector.

Ah okay, so I think this is what I was unsure about. So the mirrored transistor basically acts as a 'limiter' in that it sets the maximum current that can flow into its collector and we have set that maximum such that it is the same as the reference current? Therefore, when connected to a power source, it can fix the current in that part of the circuit. Is this correct?

Many thanks for the help.

 

[LvW]

Ah okay, so I think this is what I was unsure about. So the mirrored transistor basically acts as a 'limiter' in that it sets the maximum current that can flow into its collector and we have set that maximum such that it is the same as the reference current? Therefore, when connected to a power source, it can fix the current in that part of the circuit. Is this correct?
Many thanks for the help.

Why do you speak of a "maximim" current" and a "limiter" function?
The basic principle is simple: Two equal collector currents due to two equal base-emitter voltages.
Because any variation of the collector-emitter voltage VCE (caused by a change in the voltage across the load) will have only minor influence on the collector current (that means: Neglecting the Early-effect), we speak about a "current source" (IL) controlled/mirrored by another current (Ix).

 

[Master1022]

Thanks for your response.

Why do you speak of a "maximim" current" and a "limiter" function?

In my mind, the base current going into the right hand transistor doesn't create a collector current, but instead just allows a certain amount of current through. That is why I mention those terms, but perhaps I am mistaken.

 

[Baluncore]

In my mind, the base current going into the right hand transistor doesn't create a collector current, but instead just allows a certain amount of current through.

That is a good way to think of it. The external circuit will dictate if all the mirror current can flow. If the load has too high a resistance, then Q2 will saturate at a lower than equal current. For that reason you can think of the Q2 collector as a load current limiter.

 

[alan123hk]

It may be a bit complicated to understand the current mirror circuit through mathematical analysis.

For the sake of simplicity, I believe it can be roughly understood as follows. First, assume that Q1 and Q2 is a perfectly matched transistor pair. Because they have the same base voltage, their collector currents should be equal. The remaining question now is how to ensure that the current Ix flowing through the resistor Rx of Q1 will not change due to environmental factors (such as ambient temperature, etc.).

This is why the collector and base of Q1 are connected together. This negative feedback topology will tend to make Q1's collector voltage constant, so as long as the supply voltage Vcc remains constant, lx and the mirror current (Q2's collector current) will not change.

Please correct me if I am wrong.

 

[LvW]

The remaining question now is how to ensure that the current Ix flowing through the resistor Rx of Q1 will not change due to environmental factors (such as ambient temperature, etc.).

This is why the collector and base of Q1 are connected together. This negative feedback topology will tend to make Q1's collector voltage constant, so as long as the supply voltage Vcc remains constant, lx and the mirror current (Q2's collector current) will not change.

Please correct me if I am wrong.

Yes - of course, you are correct. When the collector current of Q1 tends to increase (due to a rising temperature), the collector voltage - and with it the base voltage - will decrease and compensates this unwanted effect.

 

[AlexCaledin]

- this mirror might be better perhaps - if all the 3 base currents are same, they do not affect the output.

 

[Baluncore]

- this mirror might be better perhaps - if all the 3 base currents are same, they do not affect the output.

Base current cancellation is often less important than thermal matching.

Current mirror accuracy usually comes down to two specific matched transistors. If those operate with different Vce, then they will differ in power and temperature.

For example, in your suggested circuit Q2 is clamped at Vce, while Q1 is subjected to 2Vce. The design and layout of mirrors that cancel base current and thermal offset voltage differences becomes progressively more involved. For every correction there is another more complex and more accurate solution.