NPN emitter degenerated current mirror

The use of emitter resistors commonly used to linearize the gain response of single-stage amplifiers. It is also employed in the design of current mirrors (e.g. our Simple bipolar current mirror) as an effective way to increase the output resistance by way of introducing negative feedback aimed to maintain the bias current constant over load voltage variations. The price paid here is the reduced headroom needed to accommodate the emitter resistor which results in a larger (worse) compliance voltage.

From the circuit above we can see that as the emitter current increases, the voltage across R2 increases, this subsequently reduces the base emitter voltage (V_be) of Q2 which then acts to decrease the emitter current, next the voltage drop across R2 decreases and V_be increases, more current flows ...etc. and the process repeats itself until a set-point is reached and loop errors are reduced.

In principle for the circuit above, because the base voltage is fixed, the process repeats itself until the voltage drop across R2 (which is proportional to our output current) remains constant and equal to the voltage drop across R1 (our setpoint, which is proportional to our current reference), with any errors in R2’s voltage (due to collector voltage dependence) subtracted from our input (V_be).

The emitter degenerated current mirror topology is a variation of the Widlar current source originally employed to allow the generation of low bias currents while circumventing the use of large integrated resistors (which otherwise consume significant layout area).

SPICE Simulations
Walking through our simulation results we have:

Operating Point Analysis
Nominally with matched output load voltage (matched Vce across output transistor), calculating the operating point DC voltages and currents for our mirror.

Relevant source code lines:

OP                      print all

* Output current over constant input current (with matched vce load): should be 1 for best match. print (v2#branch/v1#branch)

Operating point DC measurement results (re-formatted for display and analysis):

n1 = 0.96302 V n2 = 0.96302 V n3 = 0.29752 V n4 = 0.29752 V n_pos = 5.0 V v1#branch = -50.0 uA v2#branch = -49.173 uA (v2#branch/v1#branch) = 0.98346

And our relevant transistors' device parameters at the DC OP (re-formatted for display and analysis):

device     q.xq1.q1  model      qn1_npn1 ic    49.177 uA     ib    0.26456 uA     ie    -49.441 uA    vbe     0.66445 V    vbc     3.0382 mV     gm     1.8864 mS    rpi     99.569 kR     ro     1.1042 MR

device     q.xq2.q1  model      qn1_npn1 ic    49.174 uA     ib    0.26454 uA     ie    -49.438 uA    vbe     0.66445 V    vbc     3.0382 mV     gm     1.8863 mS    rpi     99.575 kR     ro    1.1043  MR

Here as before, because of the finite base current there is a small static error from the nominal reference 50uA current.

DC Analysis (Sweep)
In our DC analysis, we are measuring the variation of the mirrored output current under different loads.

We are applying a DC sweep to V2 (our load voltage) from 0 to 5V in 0.1V increments.

We are plotting the output current magnitude vs collector voltage. (our load voltage at n2)

Relevant source code lines:

DC V2 0V 5V 0.1V         ; Sweep Collector voltage from 0v to 5V in 0.1v increments.

setcs title = 'DC Analysis: Collector Current Output vs Collector Voltage (Zoom)' set filename = {$generic_prefix}{'_dc_analysis'} gnuplot $filename (v2#branch*-1e+06) ylimit $ylow $yhigh xdelta $xdel title $title xlabel $xlabel ylabel $ylabel

As can bee seen our current output over changing load has now improved compared to the simple BJT mirror presented before.



Results
In our reference example, having 6KR emitter resistors acts to reduce the output current dependence on load voltage and increases the output resistance of the mirror (see “figures of merit” section below), more specifically:


 * Error Measurement: Variation of 49.13uA to 49.51uA over an operating range of 0.6 to 5V. This is equivalent to an error of 0.38uA or 0.76% relative to the current reference.

However, the extra resistors also increase the minimum collector voltage the mirror can operate at (the compliance voltage), as we now have to account for both the voltage drop accross R2 in addition to the voltage across Q2 in saturation. Furthermore, there is the case of the base current error which has not been resolved either.

Note that we can also use resistors for negative feedback in MOS current mirrors by placing the resistors in the sources of both transistors, as shown in Source degeneration resistors negative feedback.

Output Resistance
Output Resistance Rout: 11.58 MR (from 0.6 to 5V range).

Compliance Voltage (for current mirrors)
Compliance Voltage Vmin: 0.6 V (from ground)

Toolchain
ICclopedia toolchain.

Bipolar process NPN SPICE models

Source Code
SPICE circuit netlist.

SPICE simulation testbench.