B² Spice

Case Study: Modeling Headphone Amplifiers in B² Spice

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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 R_a should equal the inverse of the triode’s transconductance, for example 10kµS would become 100 ohms, as 100 = 1 / 0.01. Setting R_a to this value ensures the widest, most symmetrical power delivery into the load impedance and the circuit’s output impedance becomes roughly: Zo = r_p / 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)