Having just designed a DAC with a single-ended classA output stage which drives high impedance headphones well, I wanted to explore options for expanding downwards the range of HP impedances that could be driven. SE classA has a brickwall limitation on output current and goes into aysmmetrical hard clip at the point where the output current equals the bias current. As a result, it needs to be designed with a specific load impedance in mind so that current clipping isn't the primary constraint - the DAC is optimized for 300ohm (Drop HD6XX). Having played in the past with transformers for HP drive I figured it was worth revisiting this area but this time around going the autoformer (rather than transformer) route.
The disadvantage of an autoformer (aka 'tapped inductor') is that there's no isolation between primary and secondary but in this application that doesn't bother us at all. The upside is better utilization of copper resource, though the degree of this advantage depends on the target turns ratio. The greatest advantage comes in near-unity ratios. i'd like to explore whether a rudimentary volume function could also be included alongside the impedance transformation.
Since I have a box full of PQ3230 core sets I figured I'd make a start with that size. A couple of months back I built a 1dB step AF (autoformer) attenuator to sit between DAC and amp using PQ3230s so it was a matter of seeing how to adapt that for HP use. Adaptation of something already extant being much easier than design from scratch. There are two main concerns when the intent is driving HPs rather than the light load of an amp's input stage. The first is - 'what are the losses in the copper?' and the second is 'what's the bandwidth?'. These two concerns are inter-related as the more turns an AF has the greater its losses and the lower its bandwidth. So one aim is to minimize the number of turns. Pushing up against that though is a third concern - 'what's the shunt inductance?' - the core material being ferrite without a sky-high mu (as permalloy for example has) this does factor. So we don't want to go too low in turns or the trafo will 'steal' too much of the output current for its own energization.
The question of the bandwidth of the AF is something that cannot easily be predicted in advance, it has to be explored empirically. In order to make a first stab at it, I loaded my 1dB step AF with a 30ohm resistor and took a look at the HF roll-off. It showed a -3dB around 5kHz, definitely not sufficient for audio. The low-pass response is a function of the AF's leakage inductance - to get a wider bandwidth we need to get that leakage L down by at the very least a factor of 4 (which would give -3dB @ 20kHz, in the ballpark but not really ideal). Rather than build an AF with half the number of turns (to get a quarter the inductance, and hence leakage inductance which is a fairly stable ratio of that) I decided to run a sim. The sim showed I can tweak the HF roll-off upwards by introducing a cap across the 30ohm, thereby gaining a dB or so in extra HF flatness. So it looks as though I just need to build an AF with half the number of turns of my 1dB step attenuator. Since that was designed to handle about 9VRMS, the HP AF will have 4.5VRMS input voltage handling which is more than enough given the DAC only outputs 2VRMS. I will go for a 4VRMS handling to have a little more bandwidth in reserve as sims don't always closely match reality in trafos.
The PQ3230 core has a cross-sectional area (Amin) of 142mm^2 which gives 161turns/volt at 20Hz. So to handle 5.6V peak at the worst-case frequency I'll need 5.6*161 = 901.6 turns. Let's go for 900. To get the required wire gauge we divide the available winding window (101mm^2) by 900 and take the square root. 0.335mm external diameter wire. Wire's sold by internal (copper) diameter so this says about 0.29mm to allow for insulation. If the wire's enamelled then allow a little more. Knowing the wire diameter needed we can estimate the total length and hence DCR and with the DCR we can check if the copper losses are going to be sensible into various HP impedances. The rule of thumb I've seen is that the driving impedance should be not greater than 1/8th of the HP impedance. So for the lowest impedance HPs this gives about 4ohm source impedance as a ceiling.
From my handy trafo design Excel crib sheet I see that PQ3230 bobbin has an average length of turn of 67mm so with 900T we'll have 60m of wire. 0.29mm wire clocks in at 0.27ohm/m so that's 16.3ohm total DCR end-to-end. Sanity check - the original 1dB step AF measured at 79ohm so we are in the region of 25% as predicted. To get the effective DCR 'seen' by the HPs we need to know the tap ratio - 300ohm down to 30ohm is sqrt(10) in voltage ratio. Whereas calculating effective impedance in transformers is easy, I'm not sure my mental heuristic works in the autoformer case so I'll run some sims as what Daniel Dennett calls 'intuition pumps' and then continue in another post.
The disadvantage of an autoformer (aka 'tapped inductor') is that there's no isolation between primary and secondary but in this application that doesn't bother us at all. The upside is better utilization of copper resource, though the degree of this advantage depends on the target turns ratio. The greatest advantage comes in near-unity ratios. i'd like to explore whether a rudimentary volume function could also be included alongside the impedance transformation.
Since I have a box full of PQ3230 core sets I figured I'd make a start with that size. A couple of months back I built a 1dB step AF (autoformer) attenuator to sit between DAC and amp using PQ3230s so it was a matter of seeing how to adapt that for HP use. Adaptation of something already extant being much easier than design from scratch. There are two main concerns when the intent is driving HPs rather than the light load of an amp's input stage. The first is - 'what are the losses in the copper?' and the second is 'what's the bandwidth?'. These two concerns are inter-related as the more turns an AF has the greater its losses and the lower its bandwidth. So one aim is to minimize the number of turns. Pushing up against that though is a third concern - 'what's the shunt inductance?' - the core material being ferrite without a sky-high mu (as permalloy for example has) this does factor. So we don't want to go too low in turns or the trafo will 'steal' too much of the output current for its own energization.
The question of the bandwidth of the AF is something that cannot easily be predicted in advance, it has to be explored empirically. In order to make a first stab at it, I loaded my 1dB step AF with a 30ohm resistor and took a look at the HF roll-off. It showed a -3dB around 5kHz, definitely not sufficient for audio. The low-pass response is a function of the AF's leakage inductance - to get a wider bandwidth we need to get that leakage L down by at the very least a factor of 4 (which would give -3dB @ 20kHz, in the ballpark but not really ideal). Rather than build an AF with half the number of turns (to get a quarter the inductance, and hence leakage inductance which is a fairly stable ratio of that) I decided to run a sim. The sim showed I can tweak the HF roll-off upwards by introducing a cap across the 30ohm, thereby gaining a dB or so in extra HF flatness. So it looks as though I just need to build an AF with half the number of turns of my 1dB step attenuator. Since that was designed to handle about 9VRMS, the HP AF will have 4.5VRMS input voltage handling which is more than enough given the DAC only outputs 2VRMS. I will go for a 4VRMS handling to have a little more bandwidth in reserve as sims don't always closely match reality in trafos.
The PQ3230 core has a cross-sectional area (Amin) of 142mm^2 which gives 161turns/volt at 20Hz. So to handle 5.6V peak at the worst-case frequency I'll need 5.6*161 = 901.6 turns. Let's go for 900. To get the required wire gauge we divide the available winding window (101mm^2) by 900 and take the square root. 0.335mm external diameter wire. Wire's sold by internal (copper) diameter so this says about 0.29mm to allow for insulation. If the wire's enamelled then allow a little more. Knowing the wire diameter needed we can estimate the total length and hence DCR and with the DCR we can check if the copper losses are going to be sensible into various HP impedances. The rule of thumb I've seen is that the driving impedance should be not greater than 1/8th of the HP impedance. So for the lowest impedance HPs this gives about 4ohm source impedance as a ceiling.
From my handy trafo design Excel crib sheet I see that PQ3230 bobbin has an average length of turn of 67mm so with 900T we'll have 60m of wire. 0.29mm wire clocks in at 0.27ohm/m so that's 16.3ohm total DCR end-to-end. Sanity check - the original 1dB step AF measured at 79ohm so we are in the region of 25% as predicted. To get the effective DCR 'seen' by the HPs we need to know the tap ratio - 300ohm down to 30ohm is sqrt(10) in voltage ratio. Whereas calculating effective impedance in transformers is easy, I'm not sure my mental heuristic works in the autoformer case so I'll run some sims as what Daniel Dennett calls 'intuition pumps' and then continue in another post.
