Bandgap Reference

Does the bandgap reference really have anything to do with the silicon bandgap voltage?

The basic idea of the bandgap reference is to obtain a low temperature coefficient voltage source by cancelling the negative temperature coefficient of the diode forward voltage with the positive temperature coefficient of differential $V_{be}$.   The difference of the $V_{be}$ of two different size but otherwise identical bipolar transistors is $\Delta V_{be} = k T /q \ln \eta$ (PTAT), where $\eta$ is the current density ratio, k=1.38e-23, q=1.6e-19.  The diode voltage tempco is about -2mV/°C; to match that, $k/q \ln \eta $ = 2m, so $\Delta V_{be}$ = 600mV at the room temp.  And the diode voltage at the room temp is also about 600mV.  So the output is about 1.2V, which they say is close to the silicon bandgap voltage (1.166V at 0K).  But the essential scheme does not really seem to depend on it.

Update:

Recently I watched a lecture by A. Paul Brokaw,  "A Transistor Voltage Reference, and What the Band-Gap Has To Do With It", 1989.  He gave the clearest explanation that I've ever seen.  PTAT ($\Delta V_{be}$) and CTAT ($V_{be}$) with the right proportion add up to the constant reference, and at 0K, PTAT is 0V and $V_{be}$ is equal to the bandgap voltage.

VG0 is the silicon bandgap voltage, Vbeo is the base-emitter voltage at temperature To. 

Logarithmic Amplifier Compensation

A logarithmic amplifier is based on the exponential relationship between the collector current and the base-emitter voltage.  It is also an opamp circuit that has a gain in the feedback path, so a unit-gain stable opamp may not be stable.  It is necessary to add phase compensation.

Here is the simple logarithmic amplifier circuit and we derive the loop gain,

We will use OP-41 as the opamp. OP-41 has a typical DC gain of 134dB and gain-bandwidth product of 500K (ω1 = 3e6).  That puts the dominant pole at about 0.1Hz.  A high order pole above 1MHz leads to a phase margin of about 77 degrees.  This is typical of an internal dominant pole compensated opamp.  As we can see the loop gain plot is shifted up, the phase margin is reduced.

We place a capacitor across the collector and the emitter as compensation.  The capacitor adds a lag network.

With the zero a decade below the cross over frequency (Rs C > 3us), this results in an improved phase margin (back to near the unit-gain phase margin).

We have ignored the junction capacitance from the npn transistor.

We compare these with simulations.  We model the opamp as a two-pole transfer function.  The input current is 1mA.  The feed back has a gain of 40 or 32dB.

The phase margin is 8° without compensation and 50° with a 22n cap.  The zero and the pole are at the estimated location of 7.2KHz and 280KHz.

The compensation can be improved, which we will discuss in a later time.

Pen Drawing Tablet

XP-Pen Star G640 drawing tablet, 6x4", 8192 pressure levels, battery free stylus with two push buttons, resolution of 5080 LPI, for $25

It works on the electromagnetic induction principle.  

From the teardowns that other people have shown on the internet, the stylus is entirely passive with a coil and capacitors, that would exclude any encoding scheme.  The working hypothesis is that the tablet will transmit a signal to excite the LC tank, the LC tank oscillates and signals get picked up by the tablet.  The working area of the tablet is a PCB with horizontal and vertical traces.  The position of the stylus is calculated perhaps by centroiding on the signal strength.

The pressure level is transmitted probably by frequency modulation.  There is a ferrite on the rod that the nib is attached and the rod is pushed on a spring.  The pressure on the nib moves the ferrite relative to the coil, changing the resonant frequency.  And pressing the button connects additional capacitor to the tank, also altering the frequency.

We will try to verify the working principle without disassembling the stylus or the tablet.  We will use a simple wire loop to pick up the signals.

Without the stylus on the tablet, we pick up some signal from the tablet.   It is possibly just a 500KHz square wave ac-coupled.

 When the pen is on the tablet, we see the oscillating LC signal. 

We can take a close look at the frequency of the oscillation,

Zooming in at the peak, we can see the difference in the rising envelop when the tablet is driving and the falling envelop when the stylus is free oscillating.

At pressure level 0, the frequency is about 506KHz, and at the max pressure of 8192, the frequency is about 530KHz.  So the circuitry has a resolution of 3Hz.  When the upper button is pressed, the frequency is 484KHz, and the lower button 464KHz.  And the frequency changes from there if pressure is applied while the button is pressed.

We can make a circuit model and run simulation to compare with the measurements.

We will design a frequency to voltage conversion circuit to extract the pressure level in a future blog.

The stylus is detected with the tip about 1cm above the tablet; there is some hysteresis on that distance.  Placing the stylus flat lengthwise on the tablet  does not work, but vertically flat widthwise works.  This is a little curious; perhaps the excitation is only generate by traces in one direction.  It may be a deliberate design choice, because the stylus can be left on the tablet without affecting other pointing devices.

When we place a ferrite toroid around the stylus, the tablet can register button clicks with buttons being click.  This implies that the presence of the ferrite toroid lowers the resonant frequency to be in the range of that of button click.