Lamps for stabilizing oscillators

Most recent update 10-9-2011

Using lamps for stabilizing oscillators

Incandescent lamps have a positive coefficient of resistance versus temperature -- as they get hotter, their filament resistance increases. They get hotter when the voltage across them increases, which causes the current flowing through them to increase, but it is not a linear relationship. Because of the increasing resistance with temperature, doubling the voltage does not double the current.

This effect is used by putting the lamp in the feedback loop of an oscillator to stabilize the output -- when in the correct location in the oscillator amplifier's feedback system, as the output voltage increases, the lamp resistance increases, which in turn lowers the gain of the amplifier, reducing the output.

Lamp resistance
As a rule of thumb, a lamp's hot operating resistance will be about 10 times its cold resistance. You can measure the cold resistance with an ohmmeter, or you can estimate the cold resistance by calculating the (approximate) hot resistance from the rated voltage and current specs.

For the #1819 lamp, for example, the voltage rating is 28V and the current rating is 40mA, making the operating resistance = 700 ohms. This means that the cold resistance will be somewhere around 70 ohms. Note that tolerances are not generally as tight for lamps as for other electrical components.

IRV curve -- the lamp's operating point curve
Lamp makers don't supply graphs or tables that show the relationship between low values of voltage and current compared to the rated values -- they are interested in light output and lamp life, not in the resistance changes at low voltages. So the way to get an estimate is to measure a lamp, and the results for one lamp will pretty well generalize for nearly any lamp. I've done this for an 1819. This plot of an 1819 lamp shows the change (vertical axis) in current (red curve) and resistance (green curve) versus the change (horizontal axis) in voltage, and is normalized to 100% of the values so that all share the same scale factor and are usable for any lamp):

A standard resistor would have a straight resistance plot line that runs from (0,0) to (100,100) on this plot -- a straight line at a 45 degree angle. That straight line defines where we need to put the operating point of the lamp -- if the rate of change of resistance is equal to or less than a resistor's, then it won't provide stabilizing feedback. If you use a straightedge to hold an asymptotic slope of 45 degrees against the green plot of resistance change, you'll see that the contact point is at about 24% of the rated lamp voltage, and at about 56% of the lamp's resistance -- that's the upper bound on the lamp operating point. Also notice in the plot above that, interpolating values, at 10% of the rated voltage, the resistance is about 3.5 times the cold R.

In an oscillator, the lamp has to be operated with a voltage that will keep the rate of change of the resistance as high as possible, at the bottom end of the curve, but won't be so low that the lamp will go to its minimum resistance in operation. A usable operating point will begin at a resistance about 1.2 times the cold resistance. For the 1819 lamp, that would be at about 100 ohms; and well up on the slope, the R will be about 200 ohms.

I've found that in oscillator use, the operating resistance of a lamp will be anywhere from about 1.2 to 3 times the cold resistance, depending on many factors, but usually at the high end of that range for both good amplitude stability and for good range of control. So for good results, we can expect to use lamps:
At about 1/10 of their rated voltage.
At about 1/4 of their rated current.
At about 2/5 of their rated hot resistance.

These rules of thumb are just that -- circumstances may require moving up or down the lamp curve depending on other factors, like not being able to find a suitable lamp, which is indeed getting harder and harder.

Which lamp in the oscillator?
Choosing the right lamp is tricky. It majorly depends on the stable output voltage of the oscillator and on the feedback loop resistor + lamp gain ratio for stable output. A significant issue is having enough resistance in the feedback loop to avoid loading of the oscillator, while having enough current flowing in the lamp to get the PTC characteristic. In general, this means using low current lamps, no matter what voltage they run at. A practical upper limit will be lamps rated for 50mA of current, and lower is almost always better. This significantly limits lamp choice.

Consider a Bridged-T oscillator. The lamp and feedback resistor are in the positive feedback loop and because the lamp is in the feedback leg, as the output increases and the lamp resistance increases, the amount of positive feedback goes down, decreasing the output of the oscillator. This example is based on a Bridged-T filter with tuning capacitors in a 10:1 ratio, so the amplifier gain for stable output is about 6, making the feedback resistor ratio 5:1 because gain = (Rfeedback + Rcommon)/Rcommon = (5+1)/1 = 6. This means that with the lamp in the feedback leg of the loop, the lamp will see 5/6 of the output voltage and the common leg resistor will see 1/6. At 10VRMS output, the voltage across the lamp will be 8.33VRMS.

If it is a Wien Bridge oscillator with 10VRMS output, then the lamp and feedback resistor will be in the negative feedback loop, with the resistor in the feedback leg and the lamp in the common leg with an operating resistance ratio of 2:1. The feedback resistor will get 2/3 the output voltage and the lamp will get 1/3, or 3.33V. So, for the Wien Bridge, the lamp may have a lower voltage rating than for the Bridged-T. A good choice might be a lamp rated for 24 or 28V and low current, between say 15 and 25mA, to keep loading on the output low.

Example 1 -- Heath IG-18
In the IG-18, a Bridged-T oscillator with 8.33VRMS on the lamp, the current will depend on the lamp's voltage rating and the resulting current flow due to resistance increase. Remember that oscillators don't have unlimited output current available, and the lower the distortion of the oscillator, the less current it will supply without causing distortion to increase, so loading by the feedback loop is a big issue.

The IG-18 uses a type 90V lamp -- the closest current commercially available lamp is a 90MB. The 90MB is rated at 90V and 30mA = 3000 ohms; the measured cold resistance is about ~~330~~ 340 ohms. At 8.33V, the 90MB has a current of approximately 7mA, for a resistance of about 1200 ohms, so Heath is running the lamp at about 3 times its cold resistance. Here, the high resistance and low current of the lamp serve to stabilize while also offering relatively low loading -- a good choice. How does the Heath IG-18 fit our rules of thumb? Its lamp is running at roughly 1/10 of its rated voltage, 1/4 of its rated current, and about 2/5 of its rated hot resistance -- a good fit.

Example 2 -- Jim Williams' lamp-stabilized Wien Bridge oscillator
In Linear Technology's Application Note 43, Figure 40, Jim Williams demonstrates the application of lamp stabilization to an opamp Wien Bridge oscillator with excellent results. He chose a type 327 lamp, which is rated for 28V and 40mA,with a hot R of 700 ohms -- the same as the type 1819 lamp in my plot above, except that the 1819 I used didn't draw as much current as the nominal rating -- lamps vary a lot from unit to unit.

The output of Jim's oscillator isn't clearly stated, but a scope photo shows a peak-to-peak swing of about 19V or 6.7VRMS. This means the lamp will have 2.23VRMS across it. So Jim is operating the lamp at 1/12 of its rated voltage. The 327 (the same as a 2187, as well as the 1819) has a hot R of 700 ohms, and a measured cold R of about 65 ohms. Jim is using a 430 ohm feedback resistor, so in this circuit, the lamp should be running at about half of that, or 215 ohms, which is 3X the cold R -- or just about where you would expect. At 2.23V and 215 ohms, the current through the lamp is about 10mA, or about 1/4 the rated current, also about what you'd expect. Another good fit to our rules of thumb.

The trouble with lamps
In a word, stability. Notice that Jim raises the issue of the thermal mass of the lamp affecting stability at low frequencies. If the lamp can heat up and cool down slightly from peak to peak of the signal, then its amplitude will vary, bouncing up and down irregularly. Jim solves this problem by using several lamps in series which have a lower voltage rating but a higher current rating, and that results in higher thermal mass of the filaments -- this means the filaments can't heat up and cool down with each cycle of the signal at low frequencies. But -- it also means a much lower total impedance in the feedback network, resulting in higher loading on the amp by the feedback network, which means that the output for good performance is now only 1VRMS instead of 7VRMS. This thermal "hunting" at low frequencies can be an issue with any lamp run at a very low current compared to its rating, or with a very low current lamp with a tiny filament -- it just won't be hot enough or stay hot enough long enough to work well at low frequencies.

Some designers opt for a DC bias on the lamp to keep it warm and this kind of works. The problem is that it restricts the dynamic range of the lamp's control over the amplitude of the osciilator and that is already a problem with lamps in general. In short, this is why designers have largely chosen AGC circuits whose parameters offer more control over time constants.

Lamp types that might serve well for oscillator stabilization
Here's a list of lamp types that you can read in a new page or download that I culled from a Sylvania miniature lamp catalog and from recent personal experience. They have different bases and bulbs depending on type, but are grouped by rated voltage. I've tried to mostly select lamps with wire terminals and miniature bayonet types, though some bi-pin types and others creep in. Be aware that in general these lamps will be expensive in small quantities, if they can be found at all.