Junk Box Curve Tracer
By Doug Bell
There's been a lot of talk on the SeattleRobotics YahooGroup about oscilloscopes lately, which reminded me of the following simple circuit that many years ago a Delco technician drew on the back of an envelope for me, when I was in junior high school. It turns an oscilloscope into a simple curve tracer. When using a multimeter, you use voltage and milliamperage measurements on powered devices, and Ohm measurements on unpowered devices. A curve tracer is to an oscilloscope as an ohmmeter is to a volt/ammeter - it provides a way to use the 'scope to test unpowered devices.
,-----------------, | ,---------, | | | | | | | | | | | | | | '---------' | | Oscilloscope | | | ,----*-------O + + O------*----, | | | V H | | | | | + | O - ---*--- - O | | | | DUT '-|------|------|-' Rref | | | - | | | | | | | | _|_ | | | | *-------' /// '------* | | | | | | '----------------------------' | | | '---------------, ,--------------' | | CCCCCCCCO ,----========= Power | CCCCCCCCO Transformer __ | | | --| \----|----' | ---| )---' | --|__/-----------Fuse--'
For this to work, your 'scope must have a way to select an external horizontal input, as opposed to the usual time base sweep.
This circuit is simple enough that you can build it whenever needed, using alligator clip leads and whatever power transformer and Rref is appropriate for testing the device under test (DUT).
The circuit produces a current vs. voltage plot of the DUT. However, the plot is flipped relative to what you're used to seeing in component datasheets - the voltage is on the vertical axis and the current is on the horizontal axis, negated. If you turn your head 90 to the left (or tip your 'scope over to the right), the current axis is up and the voltage axis is to the right, like normal.
If your 'scope is calibrated, you can read the DUT voltage as the vertical deflection directly in Volts, and the DUT current as minus the horizontal deflection in Volts / Rref = Amps. If your 'scope isn't calibrated, you could use 1% resistors, Zener diodes and constant current diodes as DUTs to calibrate the display.
The vertical input was chosen to be connected to the DUT because it usually has a higher impedance than the horizontal input, thus disturbing the voltage reading less. You may even want to include your 'scope's 10x divider probe in the circuit, so that it connects across the DUT.
If you do this, don't rely on the fact that the - side of the DUT is connected to the bottom of Rref through the shield braid of the 10x divider probe and the 'scope chassis. Run a wire as shown between the DUT and Rref so that DUT current doesn't flow through the shield braid of the probe, skewing the voltage measurement and perhaps harming the probe lead if you're running high DUT current.
The power transformer is required because both sides of the 60 Hz voltage source need to be isolated from ground, since most oscilloscopes have the low side of both the horizontal and vertical inputs connected to ground, as shown.
You can use any power transformer you have available, as long as the secondary is isolated from the primary. The original circuit passed on to me used a 6.3 V filament transformer, but I've used whatever power transformer was handy and provided sufficient voltage and current to test the DUT.
A variable voltage supply is useful - you can start at zero and increase the voltage slowly until a diode or transistor junction just knees over to test the PIV or Zener voltage.
To get a variable voltage, plug your transformer into a Variac, Powerstat, or other brand of variable autotransformer. Note that an autotransformer does not provide isolation between primary and secondary, so you need a transformer besides. Or, you might have a variable transformer, for example, American Flyer and Lionel model train transformers work fine, providing both the variable voltage and the isolation from ground.
If you don't have a variable transformer, you can connect a potentiometer (pot)
across the secondary of a transformer, then take the variable AC from one side
of the pot to the wiper. Be sure the pot can handle the power dissipation due
to ipeak as well as the current from being connected across the secondary. If
you don't have a suitable pot, you could use a rheostat (a variable resistance
without a tap) in series with the secondary. Until I could afford a Variac,
I used a 1 foot diameter, 100 Watt rheostat my Dad had gotten for use with his
model train set, in series with a 300 Watt 120V bulb.
The reference resistor Rref can be anything from a resistor out of your junk box to a decade box. The original circuit passed on to me used a 1K Ohm resistor with the 6.3V filament transformer.
If you use a rheostat (or a pot connected as a rheostat) for Rref, it's a good idea to connect a fixed resistor in series to set the maximum DUT current.
In this paper, I'll usually use a style of formulas familiar to users of the Basic computer language. This lends itself to typing by allowing the entire formula to be typed on one line, and allows multi-character variable names without using subscripts. "*" is used for the multiply operator; "^" is used for the exponentiation operator. The square root operator is replaced by the sqrt() function.
Vpeak = sqrt(2) * VsecRms
ipeak = Vpeak / Rref
Ppeak = Vpeak * ipeak = Vpeak ^ 2 / Rref
VsecRms is the transformer secondary RMS AC voltage (the voltage you measure with an AC voltmeter), Vpeak is the peak instantaneous voltage that could be applied to the DUT, ipeak is the peak instantaneous current that could be applied to the DUT, and Ppeak is the peak instantaneous power that could be applied to the DUT.
Make sure Rref is large enough to prevent excessive power dissipation in the DUT. The Wattage rating of Rref should be sufficient to handle Pavg = Ppeak / 2 continuously - this occurs when the DUT is a short. For non-inductive DUTs, the DUT will never experience Ppeak.
Pdut = Vdut * idut
= Vpeak * Rdut / (Rref + Rdut) * Vpeak / (Rref + Rdut)
= Vpeak ^ 2 * Rdut / ((Rref + Rdut) ^ 2)
Pdut is the instantaneous power dissipation of the DUT, Vdut is the instantaneous voltage across the DUT, idut is the instantaneous current through the DUT, and Rdut is the instantaneous resistance of the DUT when Vdut and idut are applied.
For a given value of Vpeak, Pdut is maximum when Rdut = Rref:
PdutMax = Vpeak ^ 2 / (2 * Rref)
This is one half of Ppeak. When Rdut = Rref, the same power is dissipated in Rref.
The DUT maximum average power is then:
PdutMaxAvg = PdutMax / 2 = VsecRms ^ 2 / (2 * Rref)
If your 'scope has a fairly low horizontal input impedance (my first 'scope had a 10K Ohm horizontal input impedance) you should include that as part of Rref, by using the formula for resistances in parallel.
For these next two formulas, I'll show the way you'd see them in a book:
1 R = --------------- ref 1 1 ----- + ----- R R hor ext 1 R = --------------- ext 1 1 ----- - ----- R R ref hor
Here's how they look in Basic:
Rref = 1 / (1 / Rhor + 1 / Rext)
Rext = 1 / (1 / Rref - 1 / Rhor)
Where Rhor is the 'scope's horizontal input impedance, and Rext is the external resistance you add in parallel with the horizontal input to get a total of Rref.
You may be familiar with the following parallel resistance formulas:
Rtot = R1 * R2 / (R1 + R2)
R1 = Rtot * R2 / (R2 - Rtot)
but the former group of formulas are easier to calculate with a calculator, since you only need to enter each resistance value once, and you can use the 1/x function. It's also much easier to extend the formula to multiple resistors in parallel:
Rtot = 1 / (1 / R1 + 1 / R2 + … + 1 / Rn)
R1 = 1 / (1 / Rtot - 1 / R2 - … - 1 / Rn)
A good way to remember these formulas is to consider that when you connect resistances in parallel, the total conductance is the sum of the individual conductances.
Conductance, G = 1 / R, R = 1 / G. So, to combine resistances in parallel, calculate the conductance of each resistance, add the conductances, then calculate the resistance of the total conductance.
In some situations, I have connected a resistor in series with the horizontal input instead of in parallel, then calculated the total of that resistor and the 'scope horizontal input impedance as Rref. This allows an Rref greater than the horizontal input impedance. It can also be useful to adjust the horizontal gain, if your 'scope's horizontal gain controls don't have enough range, or to reduce the peak voltage at the horizontal input if you're testing the peak inverse voltage (PIV) of high voltage diodes, etc. In general, you can use whatever resistor network is necessary to get the desired Rref and the desired horizontal deflection.
,---------------, | | | | | | | | | | | | | | | '---------------'
The current is zero at any voltage.
,---------------, | | | | | ----------- | | | | | '---------------'
The voltage is zero at any current.
,---------------, | \ | | \ | | \ | | \ | | \ | '---------------'
The slope of the line (with your head turned 90 to the left) is the current divided by the voltage, which is the conductance or inverse resistance.
Capacitor or Inductor (an ellipse)
,---------------, | ,---, | | / \ | | | | | | \ / | | '---' | '---------------'
A capacitor conducts maximum current when the voltage drop across it is changing the most, and minimum current when the voltage across it is changing the least.
An inductor has a maximum voltage drop across it when the current through it is changing the most, and minimum voltage drop when the current through it is changing the least.
The capacitor curve is drawn clockwise; the inductor curve is drawn counter-clockwise. If you were to connect to your 'scope's Z-axis (intensity) input a sawtooth waveform at a multiple of 60 Hz, you could tell which direction the trace was being drawn.
RL, RC, or RLC circuit
,---------------, | ,---, | | | \ | | \ \ | | \ | | | '---' | '---------------'
You can see a combination of the slanted line of a resistor and the circle of capacitive or inductive reactance.
Diode or transistor junction
,---------------, | | | | | -----, | | | | | | | '---------------'
The + lead is connected to anode of a diode, or the collector or emitter of a PNP transistor, or the source or drain of a P-channel JFET, or the base of an NPN transistor, or the gate of an N-channel JFET.
,---------------, | | | | | | | '----- | | | | | '---------------'
The + lead is connected to the cathode of a diode, or the base of a PNP transistor, or the gate of a P-channel JFET, or the emitter or collector of an NPN transistor, or the source or drain of an N-channel JFET.
,---------------, |...........:...| |__________ : | | \: | |...........\...| | | | '---------------'
Expanded trace to show the forward voltage of a diode or transistor junction.
,---------------, | | | | | -----, | | | | | |_ | '---------------'
Diode or transistor junction, showing the Zener knee as the diode begins to conduct in the reverse direction.
Regions of high DUT power dissipation
,---------------, |/////| | |----' | | | | ,----| | |/////| '---------------'
Probably the most likely portion of a trace to hit one of these regions is at the Zener knee.
If Rref is large, on the order of 100K Ohms, stray capacitance may cause the lines of a trace to become loops.
You can test the current gain of a transistor, by connecting the collector and emitter as the DUT and adding a base-to-collector resistor.
You can use this curve tracer on components in circuit, if you can isolate the device containing the component from ground, or if the component you wish to test is grounded. Make sure the device is disconnected from power. It may take some study and practice to figure out the complex pattern obtained, but it should make more sense than in-circuit ohmmeter readings, since the curve tracer is making the equivalent of a whole bunch of Ohm readings at different voltages and currents.