Peter Baxandall's class-D oscillator revisited.
Bill Sloman
and Win Hill recently pushed me to post a more detailed discussion. The
ASCII art below was created in Notepad.and looks okay there. I can't
persuade Outlook Express to display a fixed width font so this is just cut
and pasted from Notepad. Hope it works.
Peter Baxandalls class-D oscillator consists of a centre-tapped transformer
with a centre-tapped secondary to drive the switches, much like a Royer
inverter, but with a capacitor connected across the transformer to form a
resonant tank circuit with the inductance of the transformer, and with an
inductor connected from the centre-tap of the primary to the positive
supply. The inductance of the inductor L2 is typically four times higher
than the inductance of the primary winding on the transformer.
V+ _____ __________
UUUUUU |
L2 |
____ ____++____ ___
| .UUUU | .UUUU |
| L1 | |
+---------||--------------+
| C1 | |
| R1 |
| R1 |
|-| | |-|
S1 |--- -----+--- ---| S2
|-| UUU. | UUU. |-|
| R2 |
| R2 |
| | |
0V ----+-------------+-----------+
The resistors R1 and R2 provide enough gate bias to make sure that the
switches S1 and S2 have some gain at start up.
The voltage across switches is a series of raised half-sine waves, with the
peak voltage about pi times the rail voltage
__ _
/ \ /
/ \ /
V+ ------/------\----------/--- voltage at collector/drain of S1, S2
0V _____/ \________/
The voltage across the centre-tap is similar series of raised half-sine
waves, of half the amplitude. The DC level averaged across the full cycle is
V+ less any voltage drop across the resistance of the inductor L2 - that is,
there is no net DC voltage across the inductance of L2.
_ __
\ / \
V+ --\----/----\--- voltage at centre tap of L1
\ / \
0V ____ \/ ______ \/
Essentially, the inductor L2 is providing a constant current drive to the
tank circuit, which the switches turn into an alternating square wave.
Unfortunately, the inductor also carries/passes an alternating current at
twice the switching frequency
__
/ \ /
0 - -----\----/------
\__/
which leads the AC voltage across the inductor L2 by 90 degrees. This
distorts the sinusoidal voltage swing across the tanK circuit, so that the
leading edge of the half-"sine" wave is steeper than it should be, the peak
earlier and the trailing edge less steep.
It would be interesing to modify Baxandall's original circuit by adding a
pair of switches at the inductor
V+ ----+----------------
|-|
---| S3
|-|
|
+ ____ __________
| UUUUUU |
| L2 |
| ____ ____++____ ___
| | .UUUU | .UUUU |
| | L1 | |
| +---------||--------------+
| | C1 | |
| | R1 |
| | R1 |
| |-| | |-|
| S1 |--- -----+--- ---| S2
|-| |-| UUU. | UUU. |-|
---| S4 | R2 |
|-| | R2 |
- | | | |
0V ----+----R3--+-------------+-----------+
These can be used - in principle - to synthesise the same raised half-sine
waveform on the driven end of L2 as appears at the centre-tap of the primary
L1.
The amplitude of the voltage swing across L1 and C1 would drop from pi times
V+ to twice V+, less any loss in the inductor L2, and the AC voltage across
L2 would be much reduced, to a level related to the losses in the tank
circuit and the load.
In order to synthesise the half-sine wave we have to know the phase and
frequency of the signal across L1/C1 and that can most easily be picked up
by duplicating S1 or S2 with a small signal transistor and feeding the open
drain/collector output into a suitable logic gate, most likely one of the
signal iputs to a 4046-type phase locked loop. The phase-locked VCO has to
run at an appreciable multiple of the resonant frequency - 12x faster or
more - and this has to be divided down to generate the waveform which is
locked to the switch drive as well as the drive waveforms for S3 and S4.
If the VCO is run at a relatively high multiple of the resonant frequency,
we could use one of Don Lancaster's "magic sine" binary sequences to
generate our raised half-sine to drive L2, but the Baxandall circuit is
effectively a 2-pole L2,C1 filter for the voltage drive on L2 and making any
serious effort to minimise very high harmonics on the drive waveform would
be a waste of effort.
The crudest approximation to a half-sine wave would be the "modified sine
wave"
V+ __ ---- ____ --- ____ --- ___
| | | | | |
0V --+____+----+___+----+___+
which is a 0V from 330 degrees to 30 degrees and from 150 degreesto 210
degrees and a V+ for the remaining 2/3rds of the time.
__ _
/ \ /
V+ ______/____\ ___________/__
/ \ /
0V ____/ \________/
The voltage across the inductor is then rather messy
/ \ / \ / \
0V --|--|-----|--|-----|--|---
/\ /\ /\
When compared with same waveform in the orignal circuit, this messy waveform
contains a lot less second harmonic content - and by playing with the
mark-to-space ratio this might be reduced to zero - and significantly lower
amplitudes of higher harmonics.
The higher harmonics drive less current through L2 (in proportion to the
harmonic number), and this current produces smaller voltage excursion across
C1, (again in proportion to the harmonic number).
Adding extra switching transitions to the PWM waveform applied to S3 and S4
can cancel higher harmonics - Don Lancaster's "magic sine" bit sequences can
kill off everything up to about the tenth harmonic if your switches are fast
enough - but in Baxandall class-D oscillator you also have to worry about
the current being dissipated in the resistive impedances of the L!/C1 tank
circuit, and in the load that it is driving.
A truly modern version of the circuit would measure these losses, which
could be monitored on the current through R3 in the diagram above, and play
with the harmonic content and phasing of the PWM signal driving S2 and S3 to
make the current through R3 a clean raised sine, going to zero as S1 and S2
were switched. Writing to the progam to do the job would be sort of
challenging.
I've got a nasty suspicion that that if I read Pressman's "Switching Power
Supply Design"
ISBN 0-07-052236-7 sufficiently carefully - notably chapter 13 on resonant
converters - I'd find out that I am re-inventing the wheel, but superficial
reading suggests that his resonant converters are rather different.
-----
Bill Sloman, Nijmegen
Winfield Hill
>
> I've mentioned Peter Baxandall's class-D oscillator here from time to
> time, and Win Hill recently pushed me to post a more detailed discussion.
> The ASCII art below was created in Notepad.and looks okay there. I can't
> persuade Outlook Express to display a fixed width font so this is just
> cut and pasted from Notepad. Hope it works.
Works for me! Thanks very much, Bill, that's going to make for some
very interesting reading indeed, and perhaps some modeling later on...
Thanks,
- Win
amdx
persuade Outlook Express to display a fixed width >font so this is just cut
and pasted from Notepad. Hope it works.
Try, View--Text Size--Fixed. It works for me.
Winfield Hill
>
> Peter Baxandalls class-D oscillator consists of a centre-tapped transformer
> with a centre-tapped secondary to drive the switches, much like a Royer
> inverter, but with a capacitor connected across the transformer to form a
> resonant tank circuit with the inductance of the transformer, and with an
> inductor connected from the centre-tap of the primary to the positive
> supply. The inductance of the inductor L2 is typically four times higher
> than the inductance of the primary winding on the transformer.
>
> V+ _____ __________
> UUUUUU |
> L2 |
> ____ ____++____ ___
> | .UUUU | .UUUU |
> | L1 | |
> +---------||--------------+
> | C1 | |
> | R1 |
> S1 |--- -----+--- ---| S2
> |-| UUU. | UUU. |-|
> | R2 |
> | | |
> |-| S1 |--- -----+--- ---| S2
> |-| S4 | R2 |
> - | | | |
> 0V ----+----R3--+-------------+-----------+
>
> These can be used - in principle - to synthesise the same raised half-sine
> waveform on the driven end of L2 as appears at the centre-tap of the primary
Bill, I'm wondering if in practice the transformer doesn't usually have a
secondary winding for a floating output signal, with a turns-ratio / signal
amplitude suited to the application. The resonating capacitor can be moved
to this secondary. All transformers have leakage inductance. Here that can
serve to slightly isolate the primary's unattractive voltage waveforms from
the new secondary.
Thinking further about the transformer, it's generally a bit painful to
create a predictable stable magnetizing inductance value unless a fairly
large air gap is used. In fact, it's attractive to wind a perfect
transformer, quite small in size, with no gaps (maximizing the inductance),
and then add a parallel tuning inductor, properly and optimally made for
the task. This inductor will carry the high-Q currents from the resonating
capacitor. If the transformer's leakage inductance isn't high enough for
the desired isolation, a small inductor can be added between T1 and L.
. o o
. V+ o--+--||--- gnd | C |
. | BFC +----||------+
. | | ====== L |
. --||-' +---######---+
. || | |
. |-, S3 T1 '---######---'
. | =================
. | ,-----######--+--######---,
. | ==== | * | * |
. +--####--|-------------+ |
. | L2 | | |
. | | R1 |
. | '-| * | * |-'
. |-' S1 |---###-----+---###---| S2
. || ,-| ======= | ===== |-,
. --||-, S4 | T1 R2 |
. | | | |
. gnd ---+----R3--+-------------+-----------+
I like your idea of switching off L2's drive for part of the cycle, no
doubt a great improvement can be had from just a simple single-pulse
switching waveform, especially if the T1 <=> L isolation is sufficient.
Thanks,
- Win
Tony Williams
Winfield Hill <wh...@picovolt.com> wrote:
> Bill, I'm wondering if in practice the transformer doesn't usually
> have a secondary winding for a floating output signal, with a turns-
> -ratio / signal amplitude suited to the application. The resonating
> capacitor can be moved to this secondary.
Yes, the choice of which winding to resonate depends
on the circumstances. eg1, One of Baxandall's own
examples was a variable frequency oscillator, so
the transformer was a 17+17T primary, 34T load winding,
and a 214T tuning winding, to match the 500pF variable
capacitor. eg2, Wireless World published a circuit of
a tape bias oscillator. In this case the high voltage
secondary was the tuned winding.
> Thinking further about the transformer, it's generally a bit
> painful to create a predictable stable magnetizing inductance
> value unless a fairly large air gap is used. In fact, it's
> attractive to wind a perfect transformer, quite small in size,
> with no gaps (maximizing the inductance), and then add a parallel
> tuning inductor, properly and optimally made for the task.
Yes, Thomas Roddam's lead-in towards the final Baxandall
circuit is exactly this...... a conventional centre-
-tapped transformer (driven by a switched const-I)
and then the anti-resonant tuned circuit separately
across one of the windings.
> . o o
> . V+ o--+--||--- gnd | C |
> . | BFC +----||------+
> . | | ====== L |
> . --||-' +---######---+
> . || | |
> . |-, S3 T1 '---######---'
> . | =================
> . | ,-----######--+--######---,
> . | ==== | * | * |
> . +--####--|-------------+ |
> . | L2 | | |
> . | | R1 |
> . | '-| * | * |-'
> . |-' S1 |---###-----+---###---| S2
> . || ,-| ======= | ===== |-,
> . --||-, S4 | T1 R2 |
> . | | | |
> . gnd ---+----R3--+-------------+-----------+
> I like your idea of switching off L2's drive for part of the cycle, no
> doubt a great improvement can be had from just a simple single-pulse
> switching waveform, especially if the T1 <=> L isolation is sufficient.
Thomas Roddam was writing in the early days of
transistors, so his directions for improvement
were to speculate on replacing L2 with one or more
filter sections, to tune-out the even harmonics.
Thomas Roddam. Transistor Inverters and Converters.
Iliffe Books, 1963.
--
Tony Williams.
Winfield Hill
>
> Winfield Hill <wh...@picovolt.com> wrote:
>
>> Thinking further about the transformer, it's generally a bit
>> painful to create a predictable stable magnetizing inductance
>> value unless a fairly large air gap is used. In fact, it's
>> attractive to wind a perfect transformer, quite small in size,
>> with no gaps (maximizing the inductance), and then add a parallel
>> tuning inductor, properly and optimally made for the task.
>
> Yes, Thomas Roddam's lead-in towards the final Baxandall
> circuit is exactly this...... a conventional centre-
> -tapped transformer (driven by a switched const-I)
> and then the anti-resonant tuned circuit separately
> across one of the windings.
Anti-resonant?
Thanks,
- Win
Tony Williams
Winfield Hill <wh...@picovolt.com> wrote:
> Anti-resonant?
Yes. It is old term for one of the resonant
conditions of a parallel RLC tuned circuit,
the condition when the circuit is resistive.
It only matters for Q= <10, but they were more
pedantic in those days. (I think they had to
be, in order to squeeze the last drop out of
what they had to work with.)
--
Tony Williams.
Bill Sloman
> Bill Sloman wrote...
<snip>
> Bill, I'm wondering if in practice the transformer doesn't usually have a
> secondary winding for a floating output signal, with a turns-ratio / signal
> amplitude suited to the application.
Most of mine have. Peter Baxandall apparently invented the circuit as
way of driving high-turns ratio transformers to generate high DC
voltages, and he may not have bothered.
> The resonating capacitor can be moved to this secondary.
It can, but this usually makes it a higher capacitance, lower voltage
capacitor. The film capacitors I was using mostly had more voltage
rating than I needed, so putting the capacitor across the primary
saved me volume.
> All transformers have leakage inductance. Here that can
> serve to slightly isolate the primary's unattractive voltage waveforms from
> the new secondary.
Could do, I guess. I'm not sure that the leakage inductance is big
enough to do much good
> Thinking further about the transformer, it's generally a bit painful to
> create a predictable stable magnetizing inductance value unless a fairly
> large air gap is used. In fact, it's attractive to wind a perfect
> transformer, quite small in size, with no gaps (maximizing the inductance),
> and then add a parallel tuning inductor, properly and optimally made for
> the task. This inductor will carry the high-Q currents from the resonating
> capacitor. If the transformer's leakage inductance isn't high enough for
> the desired isolation, a small inductor can be added between T1 and L.
That extra inductor needs thinking about. In my applications the
complication and expense of third inductance wouldn't have been all
that attractive. In the one project where I had the time and the
motivation to be really picky, I did measure the change in resonant
frequency with temperature, and it was pretty low. I also measured the
effect of smallish changes in resonant frequency on the circuit
output, and it was even lower, so I could legitimately ignore the
effect.
>
> . o o
> . V+ o--+--||--- gnd | C |
> . | BFC +----||------+
> . | | ====== L |
> . --||-' +---######---+
> . || | |
> . |-, S3 T1 '---######---'
> . | =================
> . | ,-----######--+--######---,
> . | ==== | * | * |
> . +--####--|-------------+ |
> . | L2 | | |
> . | | R1 |
> . | '-| * | * |-'
> . |-' S1 |---###-----+---###---| S2
> . || ,-| ======= | ===== |-,
> . --||-, S4 | T1 R2 |
> . | | | |
> . gnd ---+----R3--+-------------+-----------+
>
> I like your idea of switching off L2's drive for part of the cycle, no
> doubt a great improvement can be had from just a simple single-pulse
> switching waveform, especially if the T1 <=> L isolation is sufficient.
If you really wanted to get crystal type frequency stabilitiy, you
might be able to pull the resonant frequency by playing with S3/S4,
but this is a pretty nasty idea.
-----
Bill Sloman, Nijmegen
Bill Sloman
Thanks to Tony williams for spotting the drop-off in the circuit
diagrams. R1 was intended to be returned to V+, not the centre-tap. I
must have throught that I was drawing a Royer inverter.
> V+
> V+ _____ __________ |
> UUUUUU ||
> L2 ||
> ____ ____+_____ ___
> | .UUUU | .UUUU |
> | L1 | |
> +---------||--------------+
> | C1 | |
> | R1 |
> | R1 |
> |-| | |-|
> S1 |--- -----+--- ---| S2
> |-| UUU. | UUU. |-|
> | R2 |
> | R2 |
> | | |
> 0V ----+-------------+-----------+
>
> The resistors R1 and R2 provide enough gate bias to make sure that the
> switches S1 and S2 have some gain at start up.
Tony Williams reminded me that with bipolar transistors at S1 and S2
you mostly throw out R2 - in principle it can raise your efficiency a
bit, but mostly it isn't worth the trouble.
>
> V+ ----+----------------------+
> |-| |
> ---| S3 |
> |-| |
> | |
> + ____ __________ |
> | UUUUUU ||
> | L2 ||
> | ____ ____+_____ ___
> | | .UUUU | .UUUU |
> | | L1 | |
> | +---------||--------------+
> | | C1 | |
> | | R1 |
> | | R1 |
> | |-| | |-|
> | S1 |--- -----+--- ---| S2
> |-| |-| UUU. | UUU. |-|
> ---| S4 | R2 |
> |-| | R2 |
> - | | | |
> 0V ----+----R3--+-------------+-----------+
Aplogies for the mistake.
-----
Bill Sloman, Nijmegen
Tony Williams
Bill Sloman <bill....@ieee.org> wrote:
> Thanks to Tony williams for spotting the drop-off in the circuit
> diagrams. R1 was intended to be returned to V+, not the centre-tap. I
> must have throught that I was drawing a Royer inverter.
> >
> > V+ _____ __________
> > UUUUUU |
> > L2 |
> > ____ ____+_____ ___
> > | .UUUU .UUUU |
> > | L1 |
> > +---------||--------------+
> > | C1 |
> > V+--------|-/\/\--------+ |
> > | R1 | |
> > \| | |/
> > S1 |----UUU-----+---UUU----| S2
> > <| . . |>
> > | |
> > | |
> > | |
> > 0V ----+-------------------------+
I edited your dwg back to a PB original (with transistors).
The basic idea is of a switched const-I source into a
parallel tuned circuit. The current changeover has to
be in sync with the zero crossing of the tank voltage.
But that does not coincide with zero collector current.
So the basic idea of the push-pull circuit above is that
the inductor provides the const-I, which is steered by
bottomed switches. There is a significant collector
current at switchover, so R1 provides a constant (full)
base current, which is merely steered by the feedback
winding on the inductor. There is only a few volts across
that feedback winding.
At switchover both transistors conduct. The overlap time
is made as short as possible, but there must never be an
underlap..... that would allow the inductor to try and
flyback the centre-tap of the tank-inductor.
Baxandall apparently stated that a square-wave current
into a parallel tuned circuit should produce a third
harmonic distortion of 100/8Q %, where Q= Rl/2piFL.
I think I can see that from a straightfoward Fourier
expansion of a square-wave current into a parallel RLC.
> >
> > V+ ----+----------------------+
> > |-| |
> > ---| S3 |
> > |-| |
> > | |
> > + ____ __________ |
> > | UUUUUU ||
> > | L2 ||
> > | ____ ____+_____ ___
> > | | .UUUU | .UUUU |
> > | | L1 | |
> > | +---------||--------------+
> > | | C1 | |
> > | | R1 |
> > | | R1 |
> > | |-| | |-|
> > | S1 |--- -----+--- ---| S2
> > |-| |-| UUU. | UUU. |-|
> > ---| S4 | R2 |
> > |-| | R2 |
> > - | | | |
> > 0V ----+----R3--+-------------+-----------+
If you are going to have switched modulation I wonder if
it would be more profitable to consider Baxadall's series-
-tuned alternative. That has a pair of switches that look
to be crying out for a simple quasi-sinewave modulation.
Vcc---+
|
+
S1 /
+
| L C Rl
+---////--+--||--+--/\/\-----Vcc/2
|
+
S2 \
|
+
0v---+--
A square-wave voltage into a series LCR. Switching is
in sync with the zero-crossing of the tank current,
easily sensed off Rl.
Rl is shown as a resistor to Vcc/2, merely as a reminder
of the voltage applied to the tank. Rl will normally go
to 0v, probably associated with a matching transformer.
Thomas Roddam noted that a matching transformer can be
given a known inductance, so that the tank/filter can be
turned into a constant-k half-section, with zero phase
shift at its band-centre. He gave a circuit example
of such a filter.
--
Tony Williams.
Bill Sloman
The overlap time is actually set by the edge speed of the sine wave at
0/180 degrees (when it *is* at a maximum). It isn't all that fast when
compared with the postive feedback your get around a Royer inverter at
switchover, and doesn't have to be, because C1 is keeping the voltage
between the collectors pretty low.
My feeling is that the switching will usually be slow enough that the
leakage inductance won't generate anything dramatic in the way of a
voltage spike.
Whether you use bipolar or MOS switches, you do have to bias the
switches so that both are at least slightly on when the is no energy
stored in the capacitor, otherwise the circuit won't switch on, and
that pretty much guarantees some overlap.
> Baxandall apparently stated that a square-wave current
> into a parallel tuned circuit should produce a third
> harmonic distortion of 100/8Q %, where Q= Rl/2piFL.
My feeling is that the second harmonic content of the current through
the inductor is the real problem. Baxandall's paper predates Spice by
a long time and the point about the third harmonic content of the
desired square wave of current through the inductor is one that you
can make by inspection.
Note that I'm not claiming to have modelled the circuit in Spice
myself. I've got LTSpice and SuperSpice on my computers at home and at
work (Kevin has been paid for both), but I've not had the time to try
and get into them far enough to run a simulation. Maybe after the end
of June ...
It is 35 years since I saw a copy of Baxandall's paper, and while I
could remember that it included the series dual of the parallel
resonant circuit drawn above, I couldn't remember enough about how it
was supposed to work to include a reference in my posting here. I get
exactly the same message from your picture - with modern digital
drivers S1 and S2 could do lots of clever stuff.
>
> Vcc---+
> |
> +
> S1 /
> +
> | L C Rl
> +---////--+--||--+--/\/\-----Vcc/2
> |
> +
> S2 \
> |
> +
> 0v---+--
>
> A square-wave voltage into a series LCR. Switching is
> in sync with the zero-crossing of the tank current,
> easily sensed off Rl.
>
> Rl is shown as a resistor to Vcc/2, merely as a reminder
> of the voltage applied to the tank. Rl will normally go
> to 0v, probably associated with a matching transformer.
>
> Thomas Roddam noted that a matching transformer can be
> given a known inductance, so that the tank/filter can be
> turned into a constant-k half-section, with zero phase
> shift at its band-centre. He gave a circuit example
> of such a filter.
The one thing I don't like about that circuit is that third Vcc/2
rail. We should be able to work out a single supply topology, but if
Peter Baxandall couldn't, it might just be in the too-hard basket.
------
Bill Sloman
Bill Sloman
> Tony Williams <to...@ledelec.demon.co.uk> wrote in message
news:<4bcfe71...@ledelec.demon.co.uk>...
> > In article <7c584d27.03030...@posting.google.com>,
> > Bill Sloman <bill....@ieee.org> wrote:
<snip>
That was truly dumb of me - the capacitor means that the DC level at the
point labelled Vcc/2 doesn't matter (so long as it isn't big enough to blow
the capacitor) and all that Peter Baxandall was doing was indicating the
size of the currents that would be flowing. Thirty-five years ago it took me
a while to work that out, and it has managed to trap me again ....
Thanks to Tony for setting me straight.
-------
Bill Sloman, Nijmegen