Towards a differential active crossover

Towards a differential active crossover

What is differential operation?

Asingle-ended (or unbalanced) circuit is one in which the signal is everywhere referenced to an arbitrary ground potential. In this case the signal and any noise are dealt with identically, and the common-mode rejection of the circuit is zero. The same is true of noise picked up in single-ended interconnects: noise cannot be removed from the signal without filtering.

In a balanced system the inputs and outputs are doubled up with one ("hot") providing the original signal polarity, and the other ("cold") a near-identical copy with reversed polarity. The signal at the input of the devices is referenced between the hot and cold inputs, and when the signal is derived by subtracting the two the common-mode noise can be reduced by several orders of magnitude. Balanced operation, however, only needs to have balanced connections at its inputs and outputs, and the circuitry inside may be single-ended throughout, or often simply a couple of doubled-up single-ended circuits. In these cases, there is often little improvement in rejection of power supply and induced noise over the basic unbalanced case, and we have the added disadvantage of the cost and added noise and distortion from the extra circuits.

A fully differential circuit takes the concept of balanced operation to its logical limits, so that there is no AC reference to ground level anywhere in the system, either in the connections or the electronics. This means that attenuation, for example, is made between hot and cold signal levels, instead of using a voltage divider to ground. Now - if the circuit is carefully designed and built - all induced noise and even-order distortion will be cancelled out between the two polarities, and in addition the differential circuit will draw an almost constant current from the power supply, vastly increasing its effective load regulation and common-mode PSRR. This is an ideal, and in practice it is sometimes necessary to use a ground reference: for instance to establish a DC quiescent level for the circuit, or to set the gain of a non-inverting input circuit.

Why a differential active crossover?

The active crossover I've been using for a year or two I designed to be "universal", in the sense that it can be configured as a two, three or four-way crossover with fixed frequencies (basically sub-bass to bass, bass to midrange, and midrange to treble), but with the gain and polarity of each output under the control of the user. It also includes my baffle step compensation circuit with the height and frequency of the compensating step adjustable, as well as balanced inputs and outputs,though the internal circuitry is all single-ended. For the moment I only need a two-way active crossover, as my DIY three-way speakers have a passive crossover between mid and treble. I have no immediate plans to replace my speakers, so much of the switching and circuitry in the crossover is redundant (and is likely to be detrimental to the signal), so I have been thinking for some time about building a dedicated crossover for these speakers without some of the more generalised features of this one. When I replaced the first crossover (built on matrix board with OP-27 and RC4227 opamps, and with no surplus features whatever) with the present one I did feel that the sound became less crisp and clear. My existing crossover is, on top of this, the main source of hum and noise in my system, mostly because its grounding arrangements are unnecessarily complex.

I have recently finished building Allen Wright's Realtime Preamplifier, whose hybrid (valve and transistor) circuitry is almost completely differential. The exception to this is the volume control, which is referenced to common ground; it would be difficult to have any kind of differential gain control without adding an extra active stage. This is a really elegant circuit which uses Allen's Super Linear Cathode Follower differential buffer circuit as its output stage. This is centred around a triode valve as a cathode follower, but inserts a constant current sink as the cathode load and bootstraps the anode to give a constant voltage between anode and cathode of the triode, significantly increasing the linearity of the circuit. The SLCF uses no overall negative feedback, but nevertheless offers a distortion performance on a par with op-amp circuits. Allen has published several versions of the SLCF, ranging from the earlier RTP5, which has MOSFETS as the current sink and bootstrap, and the latest RTP3D, which has a valve as bootstrap and a cascode valve/JFET current sink. He uses the SLCF in both single-ended (in the FVP and SVP) and differential mode (in the various RTPs).

Allen's brochures mention the possibility of using the line stage of the RTP in an active crossover, though there are tantalisingly no details, either on his web site or in the Tube Preamp Cookbook. John Broskie's Tube Cad site has an article on active crossovers which includes a fourth-order Linkwitz-Riley circuit using cathode followers as unity-gain buffers. With the RTP3 I am already using a differential preamp, and I have plans to build a differential power amplifier to match it, so the concept of differential operation already appealed to me. My own active crossover is, however, internally single-ended, with balanced connections only at input and outputs. Reading Allen and John's articles finally convinced me that a differential crossover without any negative feedback would be firstly relatively possible, and secondly would have at least the potential for major improvements in performance over the active crossover I use now, especially in a system with differential pre and power amps.

The bones

Differential filter circuits Here is a differential version of the popular unity-gain Sallen and Key filter circuit. The components are chosen for a Linkwitz-Riley alignment, and the crossover frequency is given by f=1/(2πRC). The triangles are unity-gain buffers, which can be op-amps in unity-gain mode or discrete valve or solid-state buffer stages. Rbias ensures the correct DC bias at the inputs of the buffers; without it, the outputs won't be tied down to any stable DC state.

The differential part comes in the fact that there is no explicit reference to ground in the filters, except for the bias resistors. The impedance of the capacitor or resistor straddling hot and cold parts of the circuit needs to be twice what the corresponding link to ground would be in a single-ended circuit, as there is a virtual ground at its centre,

A differential input stage

The filter circuit shown above will only work correctly if there is a differential signal in the two parts of the signal path: this is necessary to maintain the virtual ground at the centre of the "√2R" and "C/4" components. If one of the inputs is grounded the filter won't be correctly tuned. For this reason we need to put a differential input before the filters which will ensure that even with one of the inputs grounded the filter will be correctly fed with a differential signal.

Differential input circuit

Here is a differential input circuit which will generate a differential signal whether its input is differential or single-ended. The gain of this circuit is 1+2R/Rg. We can control the gain by replacing Rg with a potentiometer in series with a resistor - the series resistor is essential, as the input stage will not function with Rg=0, which will take the common-mode input voltage to the op-amp outside the permitted range.

Note that if the input from the preamp is already fully balanced the second stage, which subtracts the cold signal from the hot to ensure that the internal signal is differential even with a single-ended input, can be left out. In this case the gain will be reduced by a factor of two.

Differential passive compensation for the baffle step

In all of the previous crossovers I have built so far I have used an active baffle step compensation circuit, with an RC network in the feedback loop of an op-amp. For the moment I want to move away from this arrangement, partly to avoid having to use loop feedback, and partly to keep closer to the spirit of differential operation. It turns out that a passive compensation network is actually just as easy to design as an active one, and can be almost trivially adapted to work differentially.

Differential baffle step compensation circuit

On the right is a differential passive circuit that will give a first-order shelving step up at low frequencies. If the desired high-frequency attenuation is Ainf and the baffle step is s, centred at frequency fb, then

2πfbCR1=(1-Ainf)2√(s3)/2Ainf(s-1).

If Ainf=1/3 and s=3dB, then R2=R1 and 2πfbCR1=2.7068.

If we use a valve circuit with output impedance R1=25K and have a baffle step centred at 450Hz, then C=38.3nF, R2=25K and R3=19.6K.

Alternatively, if we use a solid-state circuit where we can get away with lower impedances, we can specify C=100nF and then R1=9.57K, R2=9.57K and R3=7.501K.

A complete op-amp implementation

Differential crossover circuit with op-amps

This is a little uneconomical with its component count (twenty op-amps!), as it doubles up the differential input as well as the baffle step circuit for both low- and high-pass parts of the circuit. However, this does actually reduce the complexity of either leg individually, as it allows the gain of the low-pass section to be adjusted differentially without an extra buffer. In this case the input stage for the low-pass leg has its gain variable from 1.5 to 6, while in the high-pass leg it is fixed at 3, which neatly cancels out the loss in the baffle step compensation network. I could of course have used a variable gain in one of the output stages, and used only a single differential input, but this would have required a resistor to ground in the feedback loop, so this stage would, at a stroke, have become both non-differential and non-unity-gain.

Moving to valves: getting rid of loop feedback

The RTP3 differential input circuit I started building above circuit with common-or-garden op-amps and a fairly standard power supply, but never actually finished it. By that time I had got used to the significant improvements my RTP3 preamp made, and came to the conclusion that the remaining slight constrained and airless quality of the sound of my system was likely to be the fault of the active crossover, with its multiplicity of op-amps, loop feedback and of course all those switches. I could have finished the new, much simpler, differential circuit, but I decided that my time would be more usefully spent putting plans together to build the circuit with valves as the main active elements, and to pursue the goal of discarding negative feedback entirely, as in the RTP3.

The differential input stage can be implemented with valves, using a circuit like the differential cascode stage at the right (this is actually the input stage of the RTP3's line stage). With the current sink on the cathodes, this stage should have excellent common mode rejection. The output impedance of this circuit is much higher than that of either the op-amp differential input or of the SLCF buffer, being to a very good approximation equal to the value of the anode resistors (in the RTP3C this is 25K). Instead of seeing this as a drawback, this output impedance may be used in place of the first resistor of the diffraction step compensation circuit. The gain of this stage is adjustable either through the two cathodes or by adding a shunt resistor between the anodes. Two input stages can be used, one for each of the low-pass and high-pass legs, and this will allow an attenuator to be used at the input of the low-pass stage.

The other active stages are all unity-gain buffers. My intention is to use the SLCF implementation from Allen's RTP5 preamp, which uses IRF710 MOSFETs as the current sink and bootstrap devices, for the high-pass stage, which requires one, rather than three, valves for each differential buffer. The low-pass leg is less critical for overall sound quality (and might even benefit from the generically firmer bass of transistor circuits), so I plan to use the FET-based buffer stage from Pedja Rogic's Gainclone project, which has a very similar topology to Allen's SLCF stage. This would give a total of fourteen valves, which is much more practical than the twenty or so that would be in an all-valve circuit with the full three-valve SLCF from the RTP3c, and also would need one fewer floating filament supply. This also considerably reduces the total power consumption of the circuit, which is important in these environmentally-conscious times, and will also help justify leaving the circuit powered most of the time.

Here is how I got on with this project!

Some links

The Tube Cad article

Pete Millet's active crossover project

Steve Bench's active crossover project

The Glassware active crossover

A crossover project at the T-line Speakers site

Alex Megann, November 2007

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