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I've been looking at a low power HF power amplifier for the last week or so, and it's been quite educational in many aspects. One of many things it has caused me to look at is whether the standard data sheet for a 1N400x diode is accurate when it shows the forward voltage versus current as a single curve for every member of the family from the lowly 1N4001 through the imperial 1N4007.

Before digging into the diode data, it may be useful to understand why a standard 50/60 Hz power rectifier diode is relevant to a 7 MHz solid state amplifier. The answer is to provide a temperature stable operating point for the amplifier transistor. I can't explain why without at least a few equations, so please try to follow along.

Consider the bipolar junction transistor as illustrated below.

I_C is the collector current and I_B. These are DC values, hence the use of capital letter for the subscripts, the normal convention when DC values are referenced.

For most of our amateur radio designs, we work with common emitter circuits, as illustrated above, and we use β as the design parameter. β is also known as the DC current gain, H_FE and is most often identified that way in data sheets. If a particular transistor has H_FE = 100, and if we want 10 mA collector current, we must inject 100 μA base drive into the transistor.

This deals with the βI_B portion of Equation 1. We then wish to look at the second term, (1+β)I_CBO. For a modern silicon transistor at room temperature, I_CBO is a relatively small number and, even when multiplied by (1+β) can be ignored.  For example, the garden variety small signal NPN transistor, the 2N440 data sheet provides the following information:

You might have noticed my frequent use of the phrase "at room temperature." That's because I_CBO has an exponential increase with temperature. For a silicon transistor, in theory, I_CBO doubles with every 7°C increase in temperature above 25°C, but this is generally pessimistic for most silicon devices.

Let's look at the 2N5109, a good choice for a 1 or 2 watt transmitter stage.

Worse yet, the transistor may enter thermal runaway, where the heat generated in the transistor due to the leakage current plus any intentional quiescent collector current plus signal current  increases the temperature, etc. The result can easily be a destroyed device.

A common fix to prevent thermal runaway is to decrease the transistor's bias current as the temperature increases. Now we finally get back to the 1N400x series diodes. At any particular current, the voltage across a silicon diode such as the 1N400x family, decreases about 2 mV/°C. Hence, if we derive the amplifier transistor's bias I_B from a 1N400x diode that is thermally connected to the amplifier transistor, the transistor's collector current tendency to increase with increasing temperature due to leakage current can be offset by reducing the bias current.

The figure below shows data I gathered a few days ago for a 2SC1945 RF medium power transistor, suitable for the 5 - 10 watt output level. The transistor had no RF drive applied, just a constant bias voltage sufficient to provide a quiescent current of 25 mA at room temperature. Collector voltage is 13.6 volts in this test. The transistor was mounted on a heat sink.  As the data shows, the 2SC1945's current was heading sharply upward as the the transistor heated up. Without the power supply's current limiting taking effect, the 2SC1945 would have been destroyed in a few minutes. Note how rapidly the current increases in a positive feedback mechanism, where increased temperature causes increased power dissipation, which in turn increases the temperature, once the transistor's junction reaches an elevated temperature.

I collected a sample of 5 of the following 1N400x diode types from my parts supply, as well as other diodes. All 1N400x family members are rated at 1A forward current.

• 1N4001 (50 volts reverse voltage)
• 1N4003 (200 volts reverse voltage)
• 1N4004 (400 volts reverse voltage)
• 1N4005 (600 volts reverse voltage)
• 1N4007 (1KV reverse voltage)
• HER108 (Taiwan Semiconductor "high efficiency rectifier" 1A forward current, 1KV reverse voltage)
• MJE182 NPN transistor, diode connected
• International Rectifier, 6F80, 6 ampere 800 volt stud-mount silicon power diode
   

I is the current through the diode PN junction
I_S a reverse saturation component independent of junction potential
e is the charge on an electron
V is the voltage across the diode's PN junction
k is Boltzmann's constant
T is the junction temperature in Kelvin
[e is the base of the natural logarithm, 2.7183...]

Equation 2 says that the relationship between current and voltage is exponential, and therefore if plotted on a log current axis and a linear voltage axis, it should be a straight line. This equation also explains why the diode's voltage drops with increasing temperature, of course.

More importantly for our purposes, the equation has no terms related to the diode's reverse breakdown voltage, i.e., the exact nature of the PN junction (doping, etc.) does not appear in equation 2. If we look in more detail, however, we find that in fact, there is an effect upon the diode's VI characteristics tied to various PN junction parameters. I won't provide further detail, but you can learn more about it at http://materials.usask.ca/samples/DiodeDesign.pdf. Hence, we expect that the single forward VI chart provided in the data sheets for the entire 1N400x family is an oversimplification.

And, in fact, Taiwan Semiconductor's HEP10x family datasheet shows exactly this relationship--the forward voltage drop is related to the reverse breakdown voltage. (HER108 = 1KV, HER104=300V and HER105=400V.) In general, for a constant current, the diode's forward voltage is proportional to the reverse breakdown voltage.

By applying DC to the diodes under test, the junction temperature increases, perhaps significantly, at higher current levels. For this reason, the industry standard is to measure VI with a 300 μs pulse. I don't have a suitable pulse generator and it would significantly complicate my automated data collection. The effect of the DC test protocol is to artificially decrease  the forward voltage at higher currents, due to the -2mV/°C diode slope.

My data shows no consistent trend relating breakdown voltage to forward voltage for my 1N400x samples. I suspect the reason for that is that my junkbox diodes are of disparate manufacture, both in terms of who made them and when they were made. I know some of these parts are at least 25 years old, and others are of recent manufacture. During this time, there's been an evolution of semiconductor processing, even in simple parts such as the 1N400x devices. The data (except for the HER108 parts) plots quite closely to the straight line Equation 2 predicts.

The data also shows how strange the HER10x parts are, compared with the 1N400x devices. Apparently Taiwan Semiconductor has something different in these devices. I also note considerable spread in device-to-device data for the HER108 parts. 

The revised (22 January 2008) data plot shows two additional diodes. The first is an MJE182 NPN power transistor connected as a diode. The second is a 6 ampere, stud-mount power rectifier, an International Rectifier 6F08 part. The 6F08s are old parts, although still in production. I've had these parts at least 20 years so a modern run of 6F08s might have somewhat different characteristics.

As a 6 ampere rated diode, the 6F08 is expected to have a larger PN junction area than a 1A rated diode, which will, in turn, be reflected in lower forward voltage drop at, e.g., 1A current, compared with a 1N4001, rated at a maximum forward current of 1A. The data reflects this expectation.
 

I intentionally disabled auto-range because as the 34410A changes current ranges, the burden voltage (current sensing resistor inside the 34410A) changes. (This is not unique to Agilent's 34410A, I believe.) The changing series resistance puts bumps in the data as the diode current changes with every range change. 

A critical part of temperature compensation of an RF bipolar transistor amplifier is the slope of the forward voltage versus temperature curve.  In order to characterize the 1N4005 diode, I made a simple water bath holder by milling out a cavity from a small block of solid aluminum. The white disk is Teflon. The brown wire parallel with the diode lead is a Fluke 80PK-1 Type K bead thermocouple. I use a Fluke 189 digital multimeter to read the water bath temperature with the thermocouple.

The diode is driven with an HP E3610A DC power supply, operated in constant current mode. The current is measured with a Goldstar DM7241 digital multimeter and the voltage across the diode is measured with an HP 3468A digital multimeter. I periodically stirred the water to reduce temperature gradients. Heat is provided by a small hot plate, with a large aluminum block to more uniformly distribute the heat source.
 

Most references simply state that a PN diode junction has a temperature coefficient of -2 mV/°C. The data I collected, however, confirms the more detailed PN junction analysis, which says that as the forward current increases, the temperature dependency slope reduces. My data shows an excellent fit to the linear relationship, i.e., the diode's forward voltage changes a certain amount for every degree temperature change, as illustrated by how closely the straight line regression line matches the data. However, the slope of this regression fit is not always -2.0 mV/°C.
 

However, the temperature versus voltage relationship for all three bias currents match my measured data quite closely:

In all three cases, LTspice shows a steeper slope than measured, although except for the 5.1mA case, the difference between simulation and measurement is well within my experimental error.

The data plot presented below show the effect of increasing temperature on collector current with a fixed bias voltage level. No signal is applied during this test. The temperature is of the heat sink to which the 2SC1945 is connected, and the heat sink is warmed with a combination of collector current (applied voltage 13.6 volts) and warmth from a hot air gun. The heat sink temperature is monitored by a Fluke 80PK-1 bead thermocouple and Fluke 189 digital multimeter.

The figure below may seem complicated, but it simply presents collector current versus temperature for a fixed DC bias voltage applied to the 2SC1945's base.

I ran the entire family of curves to better understand what goes on--it would be much easier to run a single constant current sweep. For example, set the collector current to the desired idle current at 20°C. Increase the temperature in, say, 20°C steps, reducing the VBE bias voltage to maintain the target idle current. By taking half-a-dozen similar measurements, you can characterize the necessary VBE slope rather easily.

If, for example, we decide that the 2SC1945 should be biased at 10 mA idle current, we can read horizontally across the 10 mA line and determine that at 20°C, VBE, the base bias voltage, should be about 636 mV. At 80°C, however, VBE must drop to 504 mV. Thus, the VBE source must have a voltage versus temperature slope of (504 mV - 636 mV) / (80°C -20°C) = -2.2 mV/°C.

The best match for this to use the 1N4005 characterized in the temperature run, biased at 5.1 mA. This meets the starting point voltage requirement rather closely (and, in fact, that's why I picked 5.1 mA as a test parameter), but the slope is 10% or so short of the required -2.2 mV/°C. Thus, we expect this particular 2SC1945 transistor biased with this particular 1N4005, set with a 5.1 mA forward current, to exhibit increased collector current with increasing temperature, although the degree of error may be acceptable.

This configuration is illustrated in the black line below. In fact, there is a moderate elevation in bias current at elevated temperatures, as the 2SC1945's target 10 mA idle current increases to around 16 mA over the full 20-100 degree C range. However, this degree of increase in idle current may well be acceptable.

To illustrate the importance of getting the diode's compensation slope to match the required slope, consider the red line in the plot. It shows the effect of setting the 1N4005's forward current at 35 mA. Although the idle collector current starts at 10 mA, it soon increases, reaching unacceptable levels at even modest temperatures.

In general, it is not possible to simultaneously meet requirements (a) and (b). Further, even if luck makes it possible to meet (a) and (b) in a particular case, we almost always will need to provide more current to the RF transistor than can extracted from the diode and still meet conditions (a) and (b). These requirements suggest a more complicated bias circuit than a simple shunt diode can provide. In fact, the bias circuit used in the test presented above uses one op-amp and current booster transistor, and decouples bias current generation from bias voltage reference. I'll write more about this later.

Pulse measurement data

In early 2008 when I measured the diode data, I didn't have a suitable method for generating a high value constant current drive pulse and hence used a continuous DC test current to develop the Vf versus If curves.

The problem with DC measurements at high currents is, as I mentioned, junction heating. A 1N4007 with a forward current of 1 ampere DC dissipates nearly one watt and the junction temperature is elevated well above room temperature. As discussed earlier, every 1°C increase in junction temperature reduces the forward forward voltage by more or less 2 mV.

The 1N400x series diodes has a thermal resistance of 100°C/watt according to Diodes Incorporated datasheet. At 1 ampere DC forward current, I measured Vf at 0.85 volts, for 850 milliwatts dissipation. With a 25°C room temperature, the test diode's junction temperature was approximately 25°C + 0.85 watts * 100°C/watt or 110°C. (The maximum permitted junction temperature according to the specification sheet is 150°C.) 

More pertinently for the subject of this discussion, the 85°C junction temperature rise reduces the forward voltage by around 170 mV. (As we've seen, the 2 mV/°C slope is a function of current, but we'll use it as an estimate.) In the absence of junction heating, therefore, the true Vf would be 1020 mV. How then do we measure the diode's Vf / If characteristics without contaminating the data with junction temperature rise?

The data sheet provides an answer; the Vf / If data is collected with a low duty cycle pulse waveform. The norm appears to be a 300μs pulse with a 2% duty cycle. Assuming the junction has sufficient thermal mass to average out the pulse heating, a 1 ampere pulse and approximately 1 volt forward voltage corresponds to a DC power of 20 milliwatts, which translates into a temperature rise of 2°C and 4 mV temperature error. These values are sufficiently low that they are negligible for our purpose.

The figure below shows the test setup. The HP8904A multifunction synthesizer outputs a variable amplitude pulse of 300 microseconds width. I've set the repetition frequency to 20 pulses per second, with a corresponding 0.6% duty cycle is.

The 8904A output drives one of two Kepco bipolar power supply / amplifiers, a BOP 100-1M for up to 1 ampere drive current or a BOP 20-10M for up to 10 ampere drive current. The BOP power supplies are run in current amplifier mode, so the 8904A's voltage pulse output is translated into a constant current pulse by the BOP amplifier. (For example, a 1 volt peak pulse from the 8904A causes the BOP 100-1M to generate a 100 mA constant current pulse.) The voltage across the diode under test is measured with a Tektronix TDS-430A digital oscilloscope.

I verified the accuracy of the constant current pulse with 1 ohm and 10 ohm resistors and found it within 2% of the nominal value.

As expected, the pulse measured data shows higher Vf for a given current level once junction heating becomes important. At 1 ampere forward current, for example, the pulse data forward voltage is elevated by an amount quite close to our 170 mV estimate. My measured data agrees closely with the data sheet, at least up to two amperes or so. At higher current levels, the data sheet shows lower forward voltage than I measured. Some of this difference may result from my choice of 0.6% duty cycle test waveform compared with the 2% duty cycle employed in the data sheet. At 5 amperes forward current, a 2% duty cycle test waveform still represents 110 milliwatts dissipation, which elevates the junction temperature 11°C, causing 22 mV or so voltage depression. The 0.6% duty cycle test waveform in contrast is 36 milliwatts, so about 15 mV of the difference is attributable to the difference in junction temperature.

There's also sample-to-sample variation amongst different diodes and my very simple test fixture is another error source.

As the data shows, at low currents the Schottky diode exhibits much lower forward drop than the silicon part. However, at higher current levels, the difference diminishes. At 1 ampere and above, for example, the Schottky has between 0.2 and 0.25V less drop. At 100 mA, in contrast, the Schottky diode has 450 mV less forward drop.