Popcorn QRP Audio PA for Receivers and Projects

Greetings!  For 2-3 years, I’ve received emails from readers seeking a simple “popcorn” discrete transistor PA to substitute for the LM386 part in their DYI projects. Readers wanted 3-4 transistors maximum & no differential amplifiers with current sources — and hopefully low distortion up to 1 watt with a ~12 VDC single supply.  

That seemed a tall order, but I did it (more or less). I’ll define ‘popcorn’ to mean that at maximum clean signal power, all harmonics are down to -50 to -55 dBc. This amp behaves well until driven to about 1.3 Watts.  I made a video that lies in the last section.

Above — The final Popcorn QRP PA.  4 transistors. Voltage gain = 28. Quiescent current = 73.5 mA.
This is a power amp designed to cleanly drive a speaker even at loud volumes.  To reduce distortion + boost stability, I applied ample local + global feedback which lowered gain. I suggest readers consider building up their AF signal voltage with low noise, low distortion, feedback-containing voltage amplifiers -- and not rely on their PA stage to make all the voltage + power gain.  Getting most of your voltage gain in your PA adds too much noise into your AF chain.

Above — An FFT of the Popcorn AF PA driven to exactly 1 Watt output power. The load = a 7.9 Ω “resistor” consisting of 3 two watt resistors in parallel. The second harmonic lies ~53 dB down.

Above — LM386 driven to 808 mW. This is the only LM386 scope trace I had where the voltage gain = 40 plus I had applied a good negative feedback network. Therefore, this practice seems a reasonable head-to-head test against the most venerable LM386. The Popcorn PA makes less distortion at 1 Watt, than the LM386 does at 0.81 W.  At 1W power, the LM386 begins compressing into a square wave.

I promote bench experiments – and developed this amp on my bench. I began with a lower power version using 2N4401/2N4403 complimentary emitter followers to drive the speakers. Push- pull drive as opposed to a single-ended PA driver seems the best way to go for decent output power. You might substitute any number of small signal BJTS such as the 2N3904 for the 2N4401 (or the PNP equivalent) in this project.

Let’s start where I began. I’ll show the development of the Popcorn AF PA and give ideas to consider in your own experiments.

TABLE OF CONTENTS

[ SECTION  1 ]   LOW POWER DEVELOPMENT VERSION
[ SECTION 2  ]  OUTPUT STAGE BIAS
[ SECTION 3 ]   FULL POWER VERSION
[ SECTION 4 ]   VIDEO

----   [ SECTION  1 ]   LOW POWER DEVELOPMENT VERSION   ----

Above — The schematic of the initial & fledgling Popcorn PA using paired 2N4401/2N4403 as the complimentary emitter followers.  In 1956 while working for RCA, H.C. Lin developed the first transistor power amp that didn’t use an output transformer. By around 1968, output transformers in solid state AF power amps had all but disappeared in professional designs.

Audio transformers suffer from non-linearity and in the case of the tiny transformers employed in cheap transistor radios of lore — these gave distortion, poor bass response -- plus very low output unless run in push-pull fashion. I suggest there are < 2 coherent reasons to use AF output transformers for solid state designs in 2023.
 
Input Stage

Without a differential pair as the input stage, I chose a PNP for the Q1 input amp with global negative feedback coming from the output rail going back to the Q1 emitter. The Q1 emitter also gets local feedback -- AC degeneration through the 330 Ω resistor. Because of all the feedback on Q1, Q2 provides most of the voltage gain and gets around double the collector current.

In all PA versions, Q1 bias gets set by a potentiometer (20K here). The pot proves necessary since all of us use a slightly different DC power supply voltages. The potentiometer allows you to optimize the Q1 bias for the lowest possible distortion with whatever DC power supply you use. When satisfied, you may remove the pot, measure it, and replace it with 1 -- or 2 series or parallel resistors to try to get as close as possible to the measured pot value. Alternately, you hard wire in a 20 – 25K trimmer potentiometer.  
In the final Popcorn PA version, I show a fixed Q1 bias resistor and a procedure how to set this value

The Q2 “stack” includes Q2 & all the parts connected to the Q2 collector going straight up to the positive DC power supply rail. Q2 serves as the main voltage amplifier. I placed a 10 Ω emitter resistor as local negative feedback to stabilize the stack against HF during development. I have not found any HF instability in the Popcorn PA with or without that 10 Ω resistor.

With the 2K Q2 collector resistor, the stack draws ~ 2.5 mA. Let’s look at some DSO outputs:

Above — DSO time domain output. The first draft PA driven to 2.01 volts peak-peak. Lovely sine wave.  Power = 64 mW.

Above — The FFT of the PA driven to 2.01 Vpp or 64 mW into a 7.9 Ω load.

Above — Left PA driven to 4 Vpk-pk [ 253 mW ] and 5 Vpk-pk [ 396 mW ]. Only the fundamental 2nd,3rd and 4th harmonics shown.  The 3rd harmonic tone starts to rise as the amp is driven to 4 Vpp. You can see the limitations of a single pair of TO-92 transistors such as the 2N4401/2N4403.

We’ve already exceeded the harmonic distortion goal for a popcorn PA amplifier. That is --- all harmonics must be down 50-55 dB at the maximum clean power

Above — FFT with PA driven to 6 Vpk-pk or 570 mW.  The 3rd harmonic is only 27-28 dB down. These TO-92 transistors are getting hot and starting to stink. Some of this distortion might be Beta droop from the high collector current plus heat.

Regardless, this seems like unacceptable distortion. You could easily hit power level this high on a strong Morse code (CW) station.
At this point, the 2N4401/4403 emitter followers seem only good enough for headphone level listening.

What can we do to try boost their linearity?
 

Technique One — Bootstrapping

Above — Boot strapping Q2.

Q2’s 2K collector resistor gets split to make a tap for a 330 µF bootstrap capacitor that provides positive phase feedback from the output rail to the collector. This raises collector impedance and reduces the loading effects of the Q2 collector resistance on the input of our 2 complimentary emitter followers. The positive feedback lowers Q2 signal drop.

Above — The FFT of the PA driven to 2.0 Vpp or 63 mW into a 7.9 Ω load. If anything, the 3rd harmonic is about the same while the rest are a bit worse. Bootstrapping is not helping here.

Above — The FFT of the PA driven to 4 Vpk-pk or 253 mW . The third harmonic is about the same without bootstrapping, while the other tones look a bit worse.

Above — FFT of the PA driven to 6.03 Vpp or 753 mW.  In this case, the harmonic distortion has improved. For example the 3rd harmonic improved by about 7 dB.  But overall, the net distortion exceeds our harmonic distortion goal.

Theoretically, bootstrapping may help and often works as well as driving the Q2 stack with a current source.  However, it doesn’t seem to work in this simple amplifier with a 2N4401/2N4403 pair.

Above — A fun FFT of what happens when you submit the 2N4401/2N4403 pair to 1 Watt power. Lots of compression, square waves & those emitter followers are smoking hot + stinking up the room.

Technique Two — Current Source

Above — I biased a single PNP to function as a current source. I set the output current as close as possible to that of the Q2 stack with the 2K collector resistor (limited by standard value resistors). The current source provides high impedance drive to the emitter follower pair. I won’t show any tracings because the current source, like the positive feedback, didn’t reduce distortion --- and in for some tones, worsened it.   I went back using a collector resistor.

Technique Three — Reducing the 2K collector resistor to 1K Ω

With the 2K collector resistor, the stack current measured ~ 2.5 mA. I measured the Q2 stack current at 4.83 mA when reducing the 2K Ω resistor in half. The results seemed unimpressive.

Above — For reference, With the 2K collector resistor driven to 3 Vpp.  [142 mW power]

Above — With 1K Q2 collector resistor driven to 3 Vpp. The 2nd harmonic improved by ~ 5 dB and the 3rd by about 4 dB.   At higher power like 500-600 mW, , the distortion was still too high for my liking. Further, the increase in amplifier quiescent current for the net reduction in harmonic content wasn’t worth it.

I’ve gone as far as I can with the simple 2N4401/2N4403 emitter followers. I’ve got to add some current gain and get some proper power followers. 

Before, we go to Section 3, the high power version of the Popcorn QRP PA -- Section 2 quickly covers output stage biasing:

----   [ SECTION 2  ]  OUTPUT STAGE BIAS   ----

2 diodes produce a voltage drop of around 1.3 volts providing sufficient bias for the 2N4401/2N4403 output emitter followers. From reading & my own experiments, the output bias may affect PA output distortion. The most obvious way is by giving crossover distortion.

Above — DSO screen capture of the low-power Popcorn PA with only 1 bias diode across the emitter follower bases. You may easily see (and hear) crossover distortion.

Above — An FFT of the 1 diode output bias with only the amp driven to 36 mW output power. The distortion dominates with odd order harmonics.

Above — FFT after adding back the 2nd output bias diode. This reduced the amplifier distortion shown above. Crossover plus output follower switching distortion pose factors we must live with. How far the output pair are biased from Class B towards Class A may also affect amplifier distortion.

However, using 2 diodes, we don’t have much control over that. You may place a small value resistor in series with 1 diode instead of using 2 diodes -- or in series with 2 (or more) diodes to change the output bias. An alternate way is to remove the diodes and replace them with a transistor.

Above — Schematic with the 2 diode bias replaced with an NPN referred to as an amplified diode or Vbe multiplier bias generator. Normally, this BJT has a trimmer resistor as R1 in the schematic for tweaking the voltage divider bias. The trimmer gets adjusted while watching the output in a test circuit to find the sweet spot of bias -– the setting that offers the lowest distortion in the output. 

I normally temporarily make R1 a trimmer pot, set the bias and then remove and measure the trimmer pot. Then I replace that with a fixed resistor such as the 1K8 Ω shown.

Since this is the popcorn PA stage, we’ll stick to plain diode biasing of the output followers.

[ SECTION 3 ]    FULL POWER VERSION

Above — Device under test. The best part about bench building is getting to use your test equipment. Glory and fun on the bench. Since I usually make 22 – 50 watt PAs, my electrolytic capacitor collection are all rated 50 volt to 100 volts. They look quite large in the Popcorn PA.

Above — Popcorn PA with DC voltages. Q1 shows fixed bias. I’ll give the bias procedure soon. The 10 Ω Q2 emitter resistor got dropped since this adds 1-2 dB of lower tone harmonic distortion under heavier drive.

I didn’t bother with the standard Zobel network in parallel with the speaker as seen in most AF PAs. This series cap + 10 Ω resistor across the speaker serves to lower the Q of the resonant peak of the speaker’s peak impedance at somewhere between 80 and 130 Hz.  While important for crossover design + function, I’ve left it out. You may need it with some speakers perhaps.

Power Followers
 

 

Above — I swapped out the TO-92 finals for some big boots.  In many lower power amps, to get current gain you’ll keep the TO-92 followers and then drive another set of power followers such as the BD139/BD140 pair. This works well and is recommended, however; we’re going full on popcorn on this project.
Thus, we’re keeping the emitter follower driving an emitter follower theme, but combining both in a packaged Darlington pair. This keep the parts count down -- plus provide the high Beta and current we seek to drive our speaker with room filling, low distortion loudness.

The TIP122/127 pair are only 1 example of packaged Darlington current amplifiers. I’ve got 3-4 other in my parts bins such as the BD94C/93C or TIP142/147 pairs – but again, usually I build higher power amps.

I bought the TIP122/127 pair for $2.30 Canadian dollars & they look husky and tough. You don’t even need to heat sink them for 12 VDC power.  If you need to heat sink them, then it's easy to do. Some readers emailed me to say they had smoked countless 2N3904/2N3906 pairs in their PA building adventures. Some soldered several in parallel to make a "power follower", etc..  

While purists may dislike a packaged Darlington pair – they seem perfect for popcorn PA stages and practice guitar amps alike. We have to add 2 more diodes to properly bias both Darlington transistors.

I added the Q2 boot strap back in. For this version, it significantly helped boost linearity from low to high power.

I kept the 1 Ω emitter resistors of the low power version. In pro audio, these are usually 0.1 or 0.22 Ω but of course, those amps are making some serious power.
In the past, I placed two or three quarter watt 1 Ω resistors of 1% tolerance in parallel to get the maximum possible output power. I left the popcorn emitter resistors at 1 Ω to ensure this project is stable for anyone choosing to experiment with it.

Play with every resistor value on the test bench. You’ll probably make a better PA than I did.

Let’s go through some FFT’s of the Popcorn PA at various drive levels:

Above — FFT at 3 Vpp. This proved the lowest 2nd harmonic tone measured @ -56 dBc. You could further experiment with the output bias, add a current source, or perhaps make other tweaks, if chasing a lower 2nd harmonic tone is your goal.

Above — FFT with the Popcorn PA driven to 6 Vpp or 570 mW.  Looks about the same as with 3 Vpp.

Above — FFT at 7.5 Vpp. Again it look similar to the Vpp = 3 or 6 FFTs.

Above — Cranking up the drive! FFT while driven to output 8.39 or 1.11 Watts. Still meets our popcorn goal of all tones down 50-55 dB at maximum clean power.

Above — FFT while driving the PA to 9.18 Vpp.  The harmonic tones are starting to rise!

Above — FFT while driven to 1.34 Watts. Things are falling apart.  Ok, let’s finish up.

Above — Set up schematic.  If your power supply is close to 12 VDC, then consider just building the fixed Q1 bias version shown earlier. However, bigger is better in PA stages. If you’ve got 13.8 or 14 VDC, then your maximum clean output power will go up. You may choose to optimize Q1 bias for a different DC supply.

In big power PA’s the DC rails are often unregulated. Fortunately, most of our ~ 12 VDC single power supplies are regulated which makes setting up the Popcorn AF PA a snap.

Terminate the output with a 10 ohm or lowish value resistor – or your bench 8 Ω load. Do not connect anything to the input.  Preset to maximum resistance, connect a 10 - 25K pot from the DC power supply rail to the Q1 base. Clip your positive voltmeter probe to the output rail and tweak the pot until your measured DC = your DC supply voltage divided by 1.82. Remove the pot and measure. Substitute the nearest standard value or place 2 in series or parallel to get close to this voltage.

If the output rail voltage lies between VCC/1.82 & VCC/2 you’ll be fine. Of course, you may experiment to find the optimal Q1 bias for your particular build -- that serves as the best way to optimize linearity.

[  SECTION 4 ]   VIDEO

I made a short video so you can hear the Popcorn PA in action. I connected it to a CD player plus my 8 inch guitar speaker and cranked it loudly to show its linearity under heavy audio drive.

I sampled at 44.1 KHz into mono using a Lewitt LCT 440 large-diaphragm condenser mic --- the same mic I use for my voice overs. I like the LCT 440 since it offers a flat bandwidth + very low added noise at a reasonably low cost.

Above — It seems better to watch this video on YouTube directly.

Addendum:

To clarify, I think the LM386 is an awfully good part. Imagine if your design team made a linear IC that went into hundreds of thousands of projects or products?  I'm a fan of the LM386 and the designers left us IC pins to add negative feedback with.

I cover this in the following blog post:

Link to my LM386 Experiments from November 2022

That 0-degree Phase Difference in Oscillators

This blog post arose from emails exchanged with a reader in 2015. The reader Frédéric — a newbie, sought to understand how the various sinusoidal oscillators worked in his circuits. He wanted explanations with little math & physics. Answering back, I realized how poor my basic oscillator theory teachings skills were. I studied up and wrote him a series of emails based on simple bench experiments. This Fall, I enhanced that content and even repeated many of the experiments. With joy and generosity, I present this content.

Introduction

Oscillators form the heart of radio frequency design & building. When you read oscillator papers written by genius electronics professionals, they might go something like this:  They start off with the Barkhausen criterion & equations (of course). Then, they may veer straight into a series of equations using vector algebra complete with upper and lower case Greek letters; radians + total admittance in rectangular coordinates and perhaps more — all mixed in gruesome equations. Then comes the inevitable root locus plot, the showing of loop gain via a third-order voltage transfer function, and then finally they may go off into byzantine filter theory using complex conjugate poles. Absolutely fabulous stuff if you’re an engineer or physics major – and yes, I do exaggerate for fun.  
 

All fun aside, understanding oscillator best practices ranks as problematic for some pros and amateurs alike since oscillators are non-linear circuits with linear aspects. You’ll find seemingly endless schematics to puzzle over. I’ve read that there are 18 or more variants of the Colpitts oscillator alone — spanning LF to terahertz.

Design & analysis of oscillators usually involves 3 basic methods:

[1] Negative resistance method using the +/-R & jX operators.
[2] Reflection amplifier method using scattering parameters & reflections (S11 and/or S22).
[3] Positive feedback loop method.  This seems the easiest way for newcomers — I’ll only discuss concepts from the positive feedback loop method.

The 2 minimal conditions according to the Barkhausen conditions:
To oscillate + sustain:  the input & output phase difference must be zero; and the whole loop gain must = 1 or greater than 1.

These are important minimal requirements. Real oscillator designers strive to achieve other goals that may include biasing for the best amplifier operating point, boosting resonator Q, lowering phase noise, and/or enhancing temperature + amplitude stability. They may work to reduce loading effects on the frequency determining circuit by the gain stage, or, perhaps, to fit the oscillator into a very tiny footprint. We’ll ignore all that stuff.

Let’s begin our minimum math discussion with the table of contents:

[ SECTION 1 ]   Phase Difference
[ SECTION 2 ]   Feedback & Function

[ SECTION 3 ]   B E N C H   E X P E R I M E N T S
  via 3 basic types of frequency determining feedback networks
   a.    Transformer
   b.    Pi phase shifter
   c.    Tuned input and output

[ SECTION 4 ] Conclusion
[ SECTION 5 ] References

---------- [ SECTION 1 ] Phase Difference ----------

Phase difference is the time interval between a discrete event occurring on 2 or more wave forms. The discrete event occurring at a point in time may be the positive peak of a sine wave, or perhaps the rising edge of a square wave, or something else. In electronics, 1 way to express time (phase) difference is in degrees.

Above — Two identical frequency sine waves. The discrete event in time is the positive peak of the sine wave. Wave A leads wave B. You might also say that B lags A.  The time difference of these 2 events relates to the phase difference between the 2.  This figure shows a very simple formula to help beginners.  

Phase difference = the time difference between the discrete event in A and B divided by the total time of 1 complete cycle. That value gets multiplied by 360 to convert it to degrees. Thus, when total time = 1 second; if the time difference = .25 seconds, the phase difference = 90 degrees.  If the time difference = 0, then the phase difference is 0 — & the 2 waves are said to be in phase.

Above — I built a simple pi filter designed to give a 90 degree phase difference at 3.58 MHz when comparing the output to the input or vice versa. A signal generator set to 3.58 MHz with a 50 Ω output impedance was connected to the filter. The filter output got terminated in the 50 Ω input of my DSO. I placed a 10X probe on the filter input to give 2 channels. The DSO output shows a 90 degree phase difference between the 2 waves at 3.85003 MHz. 

I had to tweak the frequency a little to account for real-world variances of the L C parts. We might say that the output was phase shifted 90 degrees compared to the input. The terms leads or lags with respect to 2 travelling waves might help firm up the concept of a time difference between the 2 signals in your mind.

In more advanced analysis with math, the phase difference gets characterized by a measured quantity known as a phase angle.

---------- [ SECTION 2 ] Feedback and Function ----------

Feedback

A portion of the output signal (either a voltage or a current) is connected to, or “fed back” to the input. We'll focus on voltage feedback in this presentation.

Negative feedback 

The fed back output signal has a 180 degrees phase difference with the input signal. This is called anti-phase, or inverted phase. Negative feedback bucks or subtracts from the input signal and gets called degenerative feedback. 

Positive feedback

The fed back output signal is identical in phase to the input signal. This is called in-phase or a 0 degree phase difference (it may also be 360 degrees, or multiples of 360 degrees). Positive feedback adds to the input signal — it sums with the input voltage causing the output to increase and gets called regenerative feedback.

To sustain oscillation, the feedback must be positive since apart from power supply DC, an oscillator lacks an external input signal. The oscillator amplifier output goes to a buffer for external circuitry, plus, some portion of the output goes through a frequency determining network and back to the input with no net phase difference at the oscillation frequency. E.g., a positive feedback loop at 1 frequency.
 
A proper oscillator produces a repetitive output waveform. This output waveform may be sinusoidal (sine wave) or non-sinusoidal. We’ll focus on sinusoidal or near-sinusoidal RF oscillators that use LC  inductor/capacitor circuits.

The oscillator as a filtered noise amplifier

Some impulse(s) must trigger the loop circuit to start oscillating. This might be turn-on noise, plus random noise from loop parts such as transistor thermal noise. That bit of noise loops around from output to input and starts the ball rolling.

Initially, positive feedback will cause the signal amplitude to build up and the active device will operate in it’s undistorted linear region. Eventually the rising linear oscillation amplitude will push the device into saturation and gain becomes nonlinear (distorted) & clipping + compression occurs. In its saturation region, amplifier gain tends to decrease as the signal amplitude moves towards the DC power supply voltage. At some point, the amplitude will reach steady state with stabilized or “limited” amplitude. The final amplitude depends on complex factors that may include the amplifier non-linear device characteristics and how deep into non-linear operation the gain stage goes.

Thus, at the loop frequency determined by the frequency determining circuitry, where the input and output phase difference is 0, a signal will arise having fundamental, harmonic and noise energy.
 
The loop gain criterion >=1 does not imply the amplifier voltage gain is 1 or 0 dB. The amplifier must provide enough gain to overcome circuit losses, plus have enough gain for start up — and to sustain oscillation in a variety of conditions such as adverse temperature or load changes. Further, losses may vary with the type of resonator circuit. A crystal or SAW resonator will give more insertion loss than an LC tank or pi filter at resonance.

Finally, the oscillator output harmonic distortion and stability is affected by the Q of the frequency determining network. A high Q circuit filters more sharply, so signals fall off from the resonant frequency more quickly than a low Q circuit. A high Q network also incurs less losses than a low Q circuit at resonance. The Q may also affect stability since non-linear amplifier function may vary with the degree of filtration offered by a given frequency determining network.

---------- [ SECTION 3 ]   B E N C H   E X P E R I M E N T S ----------

    via 3 basic types of frequency determining feedback networks
    [ 3a ] Transformer

   

Above — A common base BJT oscillator using transformer feedback. For the Section 3 experiments, I show minimalist, biased & functioning circuits at 1 frequency. By going with split DC supply, we enjoy a reduction in bias circuitry to allow a clear view of the frequency determining feedback network and amplifier. Each circuit employs a 10K resistor connected to the negative DC rail to provide a current source. All the circuits run between 0.8 to 1.3 mA DC current for easy comparison. To measure the emitter/collector current measure the voltage drop across either 100 Ω resistor and use Ohm’s Law to calculate current.


Above — To sample the output in my DSO, I placed 1 turn of wire through the T68-2 toroid & grounded 1 end. A 10x probe is connected to the hot end. Normally, we use a linear buffer with oscillators. Again, my approach is minimalist, so the basic oscillator circuit gets emphasized.

 

Above — Output wave forms of the common-base BJT oscillator with no 8K2 shunt resistor [left] and as shown in the schematic [right]. In most basic oscillator circuits amplitude regulation gets achieved by the BJT going into clipping — clipping maybe minimized if the BJT gain is just high enough to maintain oscillation, but you need enough gain to start oscillation and sustain it with temperature changes. In the right sided DSO tracing, the 8K2 shunt resistor reduces transistor gain and thus clipping. The only thing that stabilizes oscillation amplitude is the non-linear activity of the BJT. The powdered iron inductor measured 4.67 uH.

Above — A common gate version of the above oscillator.

Above — The DSO output of the common gate oscillator with lower distortion than the BJT equivalent. In general, like with tubes, JFET oscillators go into gain compression more gradually than a BJT, so oscillation amplitude regulation occurs with less distortion. Further, FETs offer quicker + better temperature stability, plus less heat dissipation into nearby circuitry compared to BJTs.

Above — An FFT of the common gate oscillator. The 2nd harmonic lies ~ 44 dB down. I found that the feedback coupling cap could go as low as 100 pF before it ceased to oscillate. From 100 to 200 pF the amplitude varied directly with the capacitor value.   Above 200pF it made little difference to the amplitude up to 1000 pF ( the maximum value I tried with the coupling capacitor). This capacitor mainly serves to block the negative DC voltage flowing directly to ground through the secondary winding — AC coupling. In many oscillators, capacitors are used to AC couple circuits, but may also be part of the frequency determining network.

Discussion

Shown above is the classic Armstrong transformer feedback oscillator (also called the Meissner oscillator). The feedback gets coupled via an untuned secondary winding on the LC parallel “tank” resonator. The secondary gets called a tickler by some. Feedback networks maybe manipulated to provide the correct amount of feedback, provide a phase shift and also to impedance match the input to the output.

A common base/common gate amp runs a low input impedance and quite a high output impedance which the transformer turns ratio reflects.

The common base/common gate amp provides zero phase shift from the transistor input to output. In order for the phase difference at the oscillator amplifier input to be 0, the frequency determining network must also provide zero phase shift as shown by the phasing dots on the transformer primary and secondary. The tank, a parallel resonant circuit, is 1 all experimenters should know about. In summary, at resonance, XL = XC and the impedance is maximal (considered a pure resistance).

 Above — The oscillator circuit with a common emitter (A) and common source (B) amplifier.

Above — DSO output wave forms for the (A) BJT and (B) FET oscillators. These amplifiers invert the phase of the signal from input to output (180 degree phase shift). Thus, the frequency determining network must also invert the phase. The parallel tank itself has 0 phase shift, so the secondary winding of the tank is where we perform this phase inversion. Note the polarity or phasing dots on the transformers.

Above — For newcomers to decode oscillators, a good place to start is to know whether your amplifier(s) invert the phase from input to output. A and B are op-amps shown in the inverting and non-inverting forms. When using logic gates biased as “linear amplifiers” we often employ inverters (a dead giveaway whether phase inversion happens). D shows the 3 equivalent BJT + FET circuits and whether they invert from input to output. This is something to memorize. If the oscillator contains 2 BJTs or FETs like in the Franklin oscillator, you identify whether each device inverts or not — and then trace the signal path though the loop.

Above — I built a version of the common emitter oscillator with too few secondary windings and the DSO results lie above. The oscillator starts, but then poops out because positive feedback voltage was too low in amplitude to sustain life.

On the other hand, if you make the feedback voltage too high in amplitude; depending on the amplifier type plus other factors, you may incur some bad side effects. This might include affecting amplifier input impedance and bias stability, loading the frequency determining network — or squegging. Squegging is more common in some oscillator topologies and/or oscillator amplifier types than others.

Essentially — undesirable parallel oscillations arise. A great example is motor boating in an AF power amplifier.  Too much signal amplitude excessively charges the feedback coupling capacitor and this changes the bias of the amplifier in repetitive bursts. Keeping the feedback coupling capacitor value down as low as possible is an easy way to crush squegging in oscillators where squegging might occur.

Let’s move to the second type of frequency determining feedback networks: the pi network.

 [ 3b ] Pi Phase Shifter

The humble ¼ wave pi network, whether made from L + C parts, or a transmission line such as coax or microstrip line serves as a fundamental building block in RF design. ¼ wavelength pi networks may function as impedance matcher, filter, phase shifter, frequency determining network, frequency controller, or a line balance converter just to name a few of its possible functions.

Those who work with antenna designs will get this — a ¼ wave coaxial matching transformer or stub can match a high impedance to a low impedance e.g. a capacitive reactance at 1 end may appear as an inductive reactance at the other.

The pi phase shifter is a representative feedback network for a bunch of famous oscillators. A high Q LC pi network at resonance (at its cutoff frequency peak) will function similarly to a bandpass filter. Studying the pi feedback network in the oscillators that follow may boost your insight into understanding many of the popular oscillators that are named after their inventor.

The frequency determining network of a Colpitts oscillator uses capacitive feedback, the Hartley uses inductive feedback, while the Vackar uses capacitive feedback plus a parallel LC tank. Further, these circuits may employ tapped capacitors or inductors to establish the correct feedback level at the oscillator’s amplifier input.

In a feedback loop, apart from the resonator components in a feedback loop, any stray inductance or capacitance from loop parts becomes part of the network. Of particular concern is the internal capacitances of the amplifier. Both FETS and BJTS have internal capacitances that vary directly with temperature — If temperature goes up so do these capacitances. The end result is frequency drift as temperature goes up and down. 

Designers may work to minimize this drift by various mechanisms ranging from carefully regulated DC voltage to putting the oscillator in an oven chamber. With respect to our feedback network, they might try to reduce the impact of amplifier internal capacitance by absorbing or swamping this C with external capacitors in the feedback network. The aim is to minimize the effect of device internal capacitances in determining the oscillation frequency. For example, place a large capacitor in parallel with a nearby internal capacitance to absorb it.

I’ve read that from a frequency spectrum of DC to daylight, the theoretical phase shift range for a pi network is 0 to 270 degrees. So far, I’ve only built them with a phase shift from 0 to just over 180 degrees.

Above — A low pass form pi network phase shifter is added to a common emitter oscillator amplifier at A. I changed to using a 5 pF capacitor AC coupled to a 100K resistor as a load to measure across with my 10x probe (B).  The RFC was just a random 1 mH epoxy-coated choke that was lying on my bench. I measured it at 920 µH. This choke serves only to prevent the collector AC output from passing though the 0.1 µF capacitor to ground and the value isn’t critical. 

The CE transistor amp inverts the signal, so the feedback determining network must also invert the signal. The low pass form pi network serves as a metaphor to the Colpitts oscillator. I experimented with the feedback capacitor by placing a 5-450 pF air variable cap in its place and settled on 47 pF because it gave stable and sustained oscillation. Going below 40 pF ceased oscillation. If you change any value of capacitor or the inductor value, the output frequency will change.

The most common direct example of a low-pass pi style network phase shifter is that of the Pierce crystal oscillator shown as the inverting gate oscillator in an earlier diagram. The phase shift/frequency determining network includes a crystal functioning as the resonator. The entire feedback network also includes the output resistance of the gate.

Some logic ICs such as the 74HC4060 ripple counter; or any number of microcontrollers include an inverter gate so you may wire up an RC or crystal Pierce oscillator.

Above — the DSO time domain waveform of the pi low-pass oscillator.

Above — Schematic and DSO measured output of a common emitter + high pass form pi network phase shifter. The network required an additional 0.1 µF AC coupling capacitor to prevent a DC short to ground through the left hand inductor. The series resonant frequency of that 0.1 µF cap = 6.6 MHz, so it provides a low impedance to the 7.35 MHz signal.

The high pass pi network version provides a metaphor to the Hartley oscillator. At their resonant frequency, many popular oscillator frequency determining networks resemble the circuitry & function of the pi phase shifter circuit in some form.

Above — A sidebar experiment using standard value series 100 pF capacitors that match a parallel tank to 50 Ω input & output Z at 7 MHz.

Above — A DSO trace of the above schematic showing a phase inversion. I had to tweak the frequency slightly to allow for L C variations from the design to get 180 degrees. The key point = RF filters using various topologies exhibit phase shift that changes with frequency within their pass-band, stop-band and roll-off frequency range in accordance with filter reactances & topology.  

Applying L C networks, you may manipulate filter network impedances & reactances to get a desired phase shift at a particular frequency or frequency band.

Most oscillator’s seen in amateur literature are copies of someone else’s oscillator that’s kept exactly, or perhaps scaled to another frequency. This works fine in many cases. You may also figure lots out by performing experiments on your bench, or by pursuing computer-aided design & simulation.
Actually designing oscillators for specific goals requires math + measurement that goes beyond the scope of this blog post.

Above — Frédéric pointed out I had not made a common drain nor common collector type oscillator, so I built the very simple Colpitts design shown above. It’s your job to figure out the phase shifts. Does the common collector/common drain amplifier invert the signal from input to output?

Let’s wrap up and go to the 3rd and final basic type of frequency determining feedback networks you might see in your travels.

 [ 3c ] Tuned input and output

Above — A tuned input + tuned output oscillator or TITO oscillator with a common source amp. I had to tune the gate tank since its pretty difficult to match up 2 L C tanks without at least 1 variable capacitor.
The common source JFET amp inverts the signal. The TITO uses a bandpass filter phase shift network to invert the feedback signal back to 0 phase difference at the JFET input. The bandpass filter (called a 3 element pi section in my old ARRL handbook) gives the needed 180 degree phase shift.

Above — The DSO tracing for TITO.

[ Section 4 ] Conclusion ----------

I provided a basic, non-math introduction to RF oscillators using simple but functioning designs. The same principles apply to oscillators that use a crystal, SAW, coaxial, or MEMS resonator instead of an L C type circuit.
 
[ Section 5 ]    References  ----------

The Oscillator as a Reflection Amplifier, an Intuitive Approach to Oscillator Design,” by John W. Boyles, Microwave Journal, June 1986, pp. 83–98

Lindberg, E. (2013). Oscillators - a simple introduction. In Proceedings of ECCTD 2013 IEEE

M. Gottlieb, Practical Oscillator Handbook, Butterworth-Heinemann, London, 1997

R.W. Rhea, Oscillator Design and Computer Simulation, 2nd Edition, Noble, 1995

Yasuda, T., Uchino, K., Izumiya, S., Adachi, T., & Senanayaka, S. S. (2013). 433 MHz wide-tunable high Q SAW oscillator. 2013 Joint European Frequency & Time Forum & International Frequency Control Symposium (EFTF/IFC), 744–746