Headphone Amplifiers

By John Broskie




Contents:


Introduction

Considering that almost all consumer audio electronics (VCR’s, CD players, receivers, and walkmans) come with a headphone jack, why would anyone want to build an external amplifier? The reasons are varied. Some dislike the poor sound coming from the existing headphone jack, which usually results from cheap op-amps and poor-quality electrolytic coupling capacitors. Others wish to play their headphones louder than their existing headphone amplifier can support: portable CD and MP3 players have only so much battery voltage available, much of which is often consumed by the voltage drops internal to the op-amps. For example, even an op-amp that swing within a volt of its power supply rails, can only put out half volt peaks, if the rails are +/-1.5 volts. Still others prefer the sound that the vacuum tubes bring to (or is it “reveal to”) home musical reproduction. Regardless of the motive, SPICE assists in the design of a quality headphone amplifier.

The first step is to determine what our design goals are. It doesn’t take much to drive a dynamic headphone to painful levels (electrostatic headphones are an altogether different story, of course), usually only a few volts and milliwatts are needed (2V and 100mW at very most). And since the headphones had already received an adequate (or close to adequate) signal amplitude from the preexisting amplifying device (the CD player, radio, etc) , the headphone amplifier doesn’t need to provide much gain: 2 to 4 times the input voltage is sufficient. Furthermore, the headphone presents a fairly benign load that runs from 16 to 600 ohms and is fairly immune to the amplifier’s output impedance; thus, the amplifier will need to provide no more than 100mA of peak current swing. 

On the other hand, headphones readily reveal a small amount of hum and noise that would pass unnoticed if reproduced from a loudspeaker. Furthermore, an amplifier DC offset of 1 volts, which wouldn’t hurt a loudspeaker, would easily destroy a headphone’s delicate voice coil. So, to recap: our goals are a quiet, DC offset free, 2 volt and 100mA peak output, low-gain amplifier.

 



Simple Op-Amp-based Headphone Amplifiers

Op-amps are the obvious solution, but which ones. While many op-amps could be pressed into service, a few stand out as good candidates, for example the AD822 for low-voltage power supplies is a good choice, although it will not meet our 100mA peak output current specification. The AD842 is a beefier amplifier that works with gains higher than 2, but requires a beefier power supply. If we are willing to cascade a low-output-current op-amp into a high-current unity-gain buffer, then the number of suitable op-amps grows. The advantage of this approach lies in the potential optimization of op-amps for two different tasks: low noise and high output current. Many of the FET input op-amps are wonderfully quiet: AD711, LF351, TL072, and others. And several unity gain buffers are available: AD811, BUF601, HA5002, LH002, LH0033 (discontinued, but excellent), LM310, LM6121H, LT1010, and MAX4178. The Google search words might be “Monolithic, Wideband, High Slew Rate, High Output Current Buffer.” (Because we demanding so much from the op-amp, we should return the favor and apply a small heat sink to its body.) Of course, once we find a suitable candidate, we will have to find a SPICE model for the device. The buffer’s output can be enclosed in the low-noise op-amp’s feedback loop or left independent of it. Including the buffer’s output in the loop will lower the buffer’s noise and distortion, but at the cost of an increased chance of instability at extremely high frequencies. (Download circuit version 4.2 Buffer HP amp.ckt; version 4.0 Buffer HP amp.ckt

It’s only a bit more work to design and test a discrete circuit, using only discrete active devices, although we will give up the ease and the automatic short-circuit protection offered by the op-amp. So the better approach might be to stick to ICs, but ICs have a few problems of their own. Most audio op-amps have been designed to have a minuscule idle current draw, which for the most part is a good, as this approach extends battery life and reduces heat. The disadvantage to the trickle of a quiescent current draw is that class-A operation barely exists and a lean class-AB is the rule. Because the op-amp has so great an open-loop gain, the crossover distortion is all but eliminated. But as we do not plan on powering our loudspeakers or warming our living room with a headphone amplifier, class-A operation has needlessly been discarded. Even the most extravagantly designed headphone amplifier—single-ended, class-A, constant-current source loaded headphone amplifier—is not that big a deal, as even a battery powered amplifier would give a fair battery life expectancy. On the next page is a headphone amplifier that was designed in B2 A/D Spice and shows much promise.



All FET, SE, Class-A Headphone Amplifier

The circuit above is as about straight forward as can be imagined. The first FET operates in a grounded-source configuration and its output is directly cascaded into the second FET’s grid, which is configured as a source follower. The 10k resistor that spans the output to first FET’s grid sets the feedback path. This circuit is limited in several ways, as the output voltage swing is compromised by the source follower’s resistive loading and the fist stage’s gain is relatively small because of its drain resistor’s low value. A better circuit requires a bit more complexity. Shown below is an improved version of the circuit above. (Download circuit: version 4.2 SE 9V 2N4393 HP amp.ckt ; version 4.0 SE 9V 2N4393 HP amp.ckt)

In this remade version, the drain resistor and source follower’s load resistor have been replaced by constant-current sources. Now, the fist stage can develop much more gain and the second stage can swing much larger current swings into 32-ohm loads. (The first stage’s constant-current source may seems too elaborate, but it isn’t. If truly identical FETs could be found and glued together to ensure a constant temperature tracking, then the internal coupling capacitor and its accompanying two high-valued resistors might be eliminated. But such a tight match is difficult to find, so the need for the extra components remains, as they keep the first stage’s output centered at half the battery voltage.) Well, how good is this circuit? The frequency response extends from 7Hz to 7MHz, which should be sufficient, save for all but the most demanding audiophiles.



But how clean is this FET amplifier and how much voltage and current can it swing and how much gain does have? To get these answers, we need output run a Transient Sweep test, with Fourier analysis. Rather than begin at zero time, the test is allowed to run for 1mS before the results start to be tabulated and after 3mS, the test is over. (In the real world of solder and scope probes, many thousands of milliseconds would pass before the circuit’s performance would evaluated, giving the circuit time to stabilize.) The Fourier setup is easy enough: the test is set to 1kHz and the signal source that feeds the amplifier’s input is set to .1 volt and 1kHz.

To get the graph to display Fourier analysis with the fundamental notched out (so that it only displays the harmonics’ amplitude  relative to the fundamental’s amplitude) requires defining a new plot line:

The normalized magnitude scales the fundamental and its harmonics relative to the fundamental; thus, the fundamental amplitude becomes 1 and all the harmonics are scaled accordingly. Now if we convert the normalized values to dBs, the fundamental becomes 0, as 20Log(1) = 0; and the harmonics are represented as being so many negative dB down from the fundamental.

What are the results? Not too good. The gain is a miserable 0.73 and the distortion harmonics are too high by anybody’s reckoning, the second harmonic being only –21dB down from the fundamental. What went wrong? What we have here is a perfect example of how easy it is to base a conclusion on too little evidence. The time window that we had specified, 1mS to 3mS was far too short to allow the SPICE engine to resolve the circuits inner workings, i.e. the establishing of bias points and the charging of capacitors.



If we run the test again with a much wider time window, we will get a better picture of what is going on in the circuit. So, let’s set the time aperture to span from 0 to 200mS, which is still only .2 seconds after all.

It took over 1 minute for this new test to finish on a fast machine (AMD 1800), which makes sense as many 1µS slices fit in 200mS. Now, we can see what had been going on in our circuit: the internal capacitors had to be charged to their quiescent values before the circuit’s output could settle down to 0 volts average, i.e. (Vmax + Vmin) / 2 = 0V. At the very end of the 200mS run, we see a symmetrical output swing and a much reduced distortion harmonic content (almost a hundredfold improvement), as shown below.

Is there a way to speed the test up? In fact, there is. If we click on “Show Steady State” from the “View” menu set, we get the follow results.

(The part labels and part values were turned off in the menu’s “Edit” » “Options” dialog box.) Notice that the internal coupling capacitor has no voltage across its plates and the output coupling capacitor has 4.5V across its leads. Steady-state analysis in SPICE ignores the capacitors altogether and reveals only the DC aspect of the circuit.



The next step is to double click on this capacitor to bring up the “Capacitor Properties” dialog box, so that we can fill the missing initial voltages.

Now we add 4.25V in place of 0V inside the initial conditions edit box and adjust the test setup to reflect a much narrower time window.

After running the new test, with “Use Initial Conditions” checked, we the following results:

The results closely match those from the end of the 200mS run. (The second harmonic is –57dB in graph above.) Now that our confidence in the results has been boosted and the testing time substantially reduced, we can modify and tweak the circuit to our liking. For example, the source-follower FET can be replaced by a NPN transistor, such as the 2N2222 from Zetex (Zetex makes superior transistors, which makes them the perfect choice for the golden-eared), which may improve the performance by lowering the output impedance; or the capacitor C2’s value can be tweaked to cause a slight low frequency peaking.



Because the amplifier uses a global feedback loop, it is sensitive to internal time constants. If the amplifier shifts the phase of the output too far of the mark, the amplifier becomes an oscillator, but by carefully choosing internal time constants, we can “tune” the low frequency response in much the same way as a low-pass filter’s peaking is tuned. For example, decreasing the output capacitor’s value by tenfold (47µF) causes a +4dB peak at 30Hz, as shown below.

What is the advantage to creating a peaking low-pass filter out of our headphone amplifier? Two advantage result: the first is that the output coupling capacitor value and, hence, its size (and cost) can be reduced; second, a bass boost is often needed to compensate for the thin sound most headphone produce. The remaining questions are how much peaking and at what frequency. Because the ear is less sensitive to low frequencies, it takes a few dBs of boost for us to hear the effect, say +3 to +9dB; and because little recorded music (excepting Classical and Rap) contains much information below 50Hz, 50Hz to 70Hz would be a good target frequency. B2 A/D Spice’s “Parameterized AC Sweep” test comes in handy here, as  we can specify a beginning and ending value for capacitor C2 and have B2 A/D Spice run a series of simulation with C2 incremented after each run.

It looks like the second plot reveals the right value (10µF), as its displays a peaking of +6.7dB at 58Hz. By the way, in order for this technique to work, the load impedance must remain fixed. In other words, if you use 300-ohm headphones, the peaking will be the same, but it will be at 5.8Hz, not 58Hz. Can we adjust the amount of peaking, while not altering the frequency at which the peaking occurs? No, as altering capacitor C1’s value also shifts the frequency. Still, it is much easier to tweak values in B2 A/D Spice than it is to actually de-solder and re-solder a circuit 20 times to find the right values.



Now that we have our desired frequency tailoring in place, how do we find out just how much voltage swing this amplifier can put into the 32-ohm load. The obvious way is to repeatedly increase voltage source V1’s AC magnitude until we see clipping. Alternatively, we can get fancy and run only one transient test.

Unfortunately, it isn’t possible to simply tell the SPICE engine to increase the input signal’s magnitude on each successive sweep; but there is a work around. Here’s how: we replace V1 with a “Nonlinear Dependent Voltage Source” from the “More Devices” submenu. This device B1 accepts a user-defined formula that will control the amount of voltage at its “output.” The equation we will insert is v =  v(N1,3) * v(3), which tells B1 to vary its voltage based on the voltage differential between nodes N1 and 3 (which equals 0Vdc and 0.1Vac) against the DC voltage present at node 3 (which is the parameter we will step up in value by 0.25V increments). Thus, the first sweep will give the amplifier an input signal of 0Vac, as 0.1 x 0 = 0; the next sweep, 0.025Vac; the next, 0.05Vac; the next, 0.075Vac …

Running the test gives the following results.

The sixth sweep seems to have the largest yet still clean waveform. The input signal on the sixth sweep is equal to 6 x 0.25Vdc x 0.1Vac or 0.15Vac.



Tube Headphone Amplifier

While many would love to own a $10,000 tube OTL (output transformer-less) amplifier, few are willing to spend that kind of money or endure the heat generated by such a behemoth. Still…if only we could get a taste of such amplifier in a cheaper, smaller package. This is the reasoning that quickly leads to a tube headphone amplifier. While headphones do present a nicer load than most loudspeakers, they are still a hard load for most tubes to handle directly (32 ohms is not that much greater than 8 ohms). Still, with some careful designing, we can come up with a vacuum tube headphone amplifier that meet most of our design criteria. Below is a schematic of the White cathode follower.


 

To get the best performance out of this circuit as a power amplifier, resistor Ra should equal the inverse of the triode’s transconductance, for example 10kµS would become 100 ohms, as 100 = 1 / 0.01. Setting Ra to this value ensures the widest, most symmetrical power delivery into the load impedance and the circuit’s output impedance becomes roughly: Zo = rp / 2mu. The limitation to this buffer circuit is that it can only be run in class-A, as it relies on the top triode to conduct throughout the waveform, so that the bottom triode can receive its drive signal from the top triode; no conduction, no signal.

The next step is to design a suitable input stage. If a global feedback loop is included in the amplifier’s design, the a high-gain input stage is the goal; but if loop is left out of the design, then a low-gain input stage becomes the goal. Since the previous headphone amplifier used a feedback loop, let’s leave the loop out of this design. Loading a triode with the same triode and the same unbypassed cathode resistor, yields an amplifier with a gain equal to half the mu of the triode used. Thus, if we use a triode with a mu of 20, we can expect a gain of 10. As the 12AU7 has a mu of 17 and it is readily available, let’s use it in the input stage. Below is the complete circuit. (Download circuit: version 4.2 White CF headphone amp 1.ckt ; version 4.0 White CF headphone amp 1.ckt)



How well does this amplifier work? If the initial results are to be believed, spectacularly well. Loaded with a 32-ohm load, the gain comes in at about 4 and the second harmonic is only 3.16% of the fundamental’s magnitude (with an input signal of 2V) and the output voltage is 15.6 volts peak-to-peak, which translates into .95 watts into 32 ohms! Well the results are not be believed. This time we have an example of how basing a conclusion on too little evidence can give overly optimistic results (given the choice, pessimistic results are always preferred, as it is better to be pleasantly surprised by better performance than to be disappointed by worse performance). If we widen the time window, we see the following results.

Applying the same procedure as we did before will straighten out the results. First we find the steady-state conditions and then we plug all the capacitors’ voltages into their initial condition edit box.

So capacitor C1’s intuitional voltage becomes 199V; C2’s, 2V; and C3’s, 102V. Now if we redo the tests, we will get some truer results. Unloaded, the gain comes in at about 8 and the second harmonic is only 0.22% of the fundamental’s magnitude (with an input signal of 0.2V). Loaded with a 32-ohm load, the gain drops to only 0.76 and the  second harmonic climbs to 5.4%. With a less excruciating load, 300 ohms, the gain becomes 4.1 and the second harmonic drops to 1.7%. If a sufficiently large input signal is applied, the amplifier will clip, which reveal the class-A boundaries of operation.

The biggest negative going voltage swing into a 32-ohm load is about 0.7 volts, which makes as it equals twice the idle current against the load impedance. (If a phase splitter were added and a conventional totem-pole output stage implemented, the peak output swing would easily double, as the amplifier could operate in class-B.) Figuring out the amplifier’s PSRR figure requires grounding the input and placing an additional voltage source in series with the power supply voltage source. 



The DC voltage is set to 0V and the peak amplitude of the AC signal is set to 1V. We can change the frequency to 100Hz or 120Hz to mimic an actual power supply’s noise frequency, but as the Fourier analysis is already set to 1kHz, we will leave that value in place. Now we run a “Transient and Fourier” test on our circuit (with a 300-ohm load).

To convert the Fourier graph to a PSSR graph, we need to define a new plot line: db(mag_v11). Looking at this new plot reveals that the PSRR figure for this amplifier is –20dB (if the AC voltage source’s voltage doesn’t equal 1 volt, the results will be wrong, as 1V is the reference voltage). Now, while –20dB is not that not great, isn’t that bad either, but it does imply the need for a well-filtered power supply or even a regulated power supply. As for the frequency response, it is plenty wide (within 1 dB from 10Hz to over 100kHz), as can be seen below.

In fact, capacitor C3’s value is needlessly too high for a 300-ohm load; 47µF would be a better value. However, if you plan on playing a variety of headphones on this amplifier, then keep the original value, as it is needed for the 32-ohm headphones. Really, the moral of this story is that driving a 32-ohm load requires using multiple output triodes in parallel, say three 6922s, to increase the gain and lower the distortion and output impedance. But with 300-ohm loads, this tube headphone amplifier will please many picky listeners.



Tube-Transistor Hybrid Headphone Amplifier

One last circuit to ponder, a vacuum tube driving cascading emitter followers. A feedback loop is used to lower the gain and the distortion of the amplifier. The power supply voltage is a mere 12.6 volts. A further trick here is the use of the tube’s heater as a load for the final transistor. This load gives us the ability to drive 32-ohm loads easily and it makes use of the current that would have to flow into the heater anyway, so we save some energy (battery time). (Download circuit: version 4.2 Tube Hybrid headphone amp 1.ckt ; version 4.0 Tube Hybrid headphone amp 1.ckt)

What happens when the tube is still cold and not conducting any current? How will the output stage handle a free-floating reference voltage? Or what will happen if the tube is not in its socket? To overcome these potential problems and other possible problems, it is best to give the first transistor’s base a fixed reference voltage. Adding two 100k resistors does the job nicely.

These resistors are large enough in value not to load-down the tube input stage and low enough in value to ensure that the output stage is biased correctly at turn on. The frequency response for this amplifier is shown below.



Conclusion

Once again we see how well B2 A/D Spice works at solving our design problems. With it we can easily evaluate the result of using different parts and different values. By using a few tests, we were able to determine peak output voltage swing, distortion, PSRR, and frequency response. For more circuits and ideas, visit the http://www.headwize.com site, which is devoted to headphones and headphone amplifiers.