# Current mirror improvement by adding resistors

One of the limitations of the current mirror with 2 BJTs is the Early effect. According to the Art of Electronics 2nd Ed., adding emitter resistors should make the circuit "a far better current source" (picture left), but I cannot see any significant difference with the circuit on the right side of the picture in terms of current stability due to Early effect. Is there any better or more formal explanation why the former circuit is preferred?

simulate this circuit – Schematic created using CircuitLab

• Try also simulating with different values for beta in each transistor. – user_1818839 Nov 24 '15 at 17:10

Early effect on the output current is helped by emitter degeneration- it's negative feedback so it increases the output resistance. I have used this to produce some precise current ramps that would not be possible using an ordinary op-amp (too fast for the op-amp to respond).

If there is a tiny difference, a fraction of a degree C, between the junctions of Q3 and Q4 you will see a large difference in the collector currents. The Vbe will not be perfectly matched to begin with either. This is much less of a problem when the transistors are part of a monolithic circuit (inherently matched) and are side-by side (or perhaps consist of multiple transistors interleaved physically and electrically in parallel pairs). Still there will usually be some difference in power dissipation between the two transistors so that will cause a gradient and some Vbe change.

For example, if the collector current is 1mA, the transconductance of the transistors will be about 0.04 mho at room temperature, so 2.5mV difference in Vbe (about 1°C) would cause about a 10% error in the collector current. Beta has a relatively small effect (assuming the transistors have a beta in the hundreds).

The Early effect will cause a reduction in the output resistance. Since the Early voltage is normally ~100V (see SPICE models for the relevant parts) the output resistance will be about 100K$\Omega$ in this case, so pretty good. With the emitter resistors as shown it will be several M$\Omega$.

Early effect can be combated by using the 4-transistor improved Wilson current mirror configuration. With discrete parts and for low frequencies, it's easier to just throw an op-amp at it.

Check out the hybrid-pi model for more insight, and try some sims with a small base voltage added to one of the transistors.

I always use resistors because without them small Vbe spreads ,changes cause large current changes .Remember the exponential term in the Ebers moll equation. Q1 & Q2 in general wont dissipate the same power so there will be Vbe differences due to Tj differences anyway.So as a rule of thumb use resistors when designing with discretes which is what I do .There are SMD matched transistor pairs that should work with no balancing resistors but I have not tried these in any high accuracy applications yet . When others design ICs its easy to keep the variability in Vbe low by running low currents and much better thermal contact and better matched silicon.Also resistors are generally harder to do than transistors when ICs are fabricated.

Try add a load resistor (1K) and run a simulation again. Because Q2/Q4 collector current is 0A. Also try to use 2N2907 as a Q2 and Q4