The K Multiplier - An
Economical Supercell Circuit
The basic circuit is at once simple and
super-effective. Film and low-ESR decoupling can be used with it and
it will not oscillate. Is there another circuit that is as effective
with a comparable parts count?
updated Oct 23, 2017
PCB available!!! - Click here!
circles, designing analog circuits for good supply noise tolerance is
the accepted norm. But home experimenters have found that
low-noise power supplies present the ultimate freedom to test out their
inexhaustible creativity. The extra degree of freedom gained from clean
power allows for less distractions from the ultimate goal of a
good-sounding circuit. So audio hobbyists have been hard at work for
decades refining the art of quiet, inert power supplies. Along these
lines several super-high performance solutions are available from the
DIY community. Many of them are very complex, needing performance opamps
and many discrete devices. But as is often the case, increasing
complexity tends to give diminishing returns. For this reason the
simplest solutions are popular to hobbyists. My circuit is a bit simpler
than most, but I see few competitors where parts count, cost and ease of
assembly are concerned.
use the positive circuit to explain. Q1 and Q2 can be recognized by most
amp designers as a Complementary Follower Pair, CFP for short. This
arrangement provides dramatically reduced output impedance and
equivalent current gain to a Darlington arrangement - just what we want
for a power source. Both transistors need at least 1.2V Vce to work
best, which is what the triple diode string D1 is for. Q2 needs more
than Q1, so I've chosen 3 diodes for 1.2V. This may seem wrong to you,
but consider that the only current through these diodes is the base
current of Q1. Diode forward voltage is roughly 400mV in the uA range,
following the 60mV/decade rule. Q1 is biased at about 15mA, which
generally gives the lowest output impedance.
D2 and R8 determine the turn-on time, and limit how much current the
circuit will dump into proceeding supply capacitors. This was important
for one builder who employed a morbidly gratuitous reservoir array. The
first time he flipped the power switch the transistors would blow from
the inrush current! It took a few tries for me to realize the problem...
If your circuit does not have inrush current over 1A, and this can be
verified in simulation, you do not need R8 and can bypass it. D3
discharges C1 when power is lost so it doesn't discharge through Q1 - do
The BC337/327 pair are crucial
to this design - they set the upper limit on input rejection. I got
input rejection using these of about 66db for the positive circuit and
54db for the negative circuit (measured in real life). BC550C/560C are
second-best in this regard. ALL high-voltage transistors I have seen
have bad quasi-saturation behavior and should be avoided for low-Vce
applications (2N5551, 2SC1845, etc).
- Input rejection: +66db/-54db
- Output impedance:
- 27mR at 100mA
- 20mR at 200mA
- 17mR at 400mA
- Excess output inductance (in inches of wire): at or below 1.
- Output current: 1.4A max
continuous. 20-400mA max for linear operation.
- Output voltage: Limited to
the Vcemax of Q1, but see Other
Adaptations for a version for any voltage.
- Voltage drop: ~1.8V (can be
less but this gives good operation)
- Max input ripple before
saturation: 1.5V pk-pk (0.46Vrms on an AC multimeter)
Advantages of the Kmultiplier
we say that the output impedance of the Kmultiplier is equivalent to
that of electrolytics, we establish a baseline to consider its
advantages. One incontrovertible advantage over electrolytics is that
the Kmultiplier has low impedance into the subsonic range. A comparable
lytic in this regard would be huge, and would necessitate soft-start
circuitry to prevent the massive inrush from destroying the preceding
wiring. Clearly the Kmultiplier provides an expediency that no capacitor
The average electrolytic 470uF and up has lower than 50mR ESR. I have
measured this figure repeatedly on lytics pulled out of broken modern
entertainment devices such as computer monitors, TVs, and power amps.
The best have less than 20mR. So the output impedance of this very
simple circuit fares very well in practical terms. The fact that this
circuit has output impedance comparable to modern lytics AND will
tolerate film and low-ESR bypass shows that I have struck a good balance
- output impedance is not any lower than is actually needed, but is low
enough to augment and seamlessly integrate with a good bypassing and
The voltage overhead of the Kmultiplier is low, making it a persuasive
drop-in addition to circuits which don't need DC regulated rails but
would benefit from heavy power filtering. In this case the Kmultiplier
replaces an oversized transformer and banks of capacitors, making it a
truly economical and expedient solution.
Because the Kmultiplier has no more feedback than needed and is
self-limiting in bandwidth, the compensation capacitors are merely those
parasitically included with the transistor junctions. This meager amount
of capacitive stress means that the circuit is unlikely to glitch even
with very fast load transients. Many regulators will emit a highly
distorted output signal when stressed with fast load current swings,
which can get into circuitry and make things worse than if the supply
was not regulated. The Kmultiplier however remains faithful into the
hundreds of KHz. Of course, why even risk high-speed signals at the
regulator when you can apply liberal decoupling across the load without
fear of oscillation?
- Choosing Components
R1 and the ESR of C1 form a resistive divider that limits the
PSRR from the outset. Luckily, a cap with 100mR ESR as C1 will
reduce PSRR by 1/5 in the worst-case scenario. The average cap
in the 1000u rage has >50mR ESR, and going below this gives
diminishing returns, so most noble brands should be safe.
Resistor type will not affect the performance of the Kmultiplier
significantly, unless maybe they are inductive. Film resistors
will be fine.
- Dissipation and heatsinking
the exceedingly low Vce of Q2 it does not need a heatsink; it
will hit Icmax before dissipation reaches 2W.
- Controlling inrush current
inrush of over 1A can destroy Q2, and often the LED as well. The
RC filter gives us a convenient and simple way to manage inrush.
At turn-on the full supply voltage minus the LED and diode string
voltage is imposed across R8. Thus if you have a 30V input, R8
will see about 25.2V. This gives C1 a max charging current of
25.2V/680R or 37mA. Because the output follows the RC voltage,
this means that for every 820uF of capacitance at the output,
there will be 37mA of inrush. So say you have 4700uF at the
output. (4700uF/820uF)*37mA gives us about 212mA.
the circuit above, use this equation to find out what value of R8
you will need to stay below 1A: (Vin-4.8)/(1A/(Cout/C1)) where
Cout is your TOTAL output capacitance.
- Output impedance depends on output
- This regulator exhibits diodic output impedance. This means
output impedance decreases with increased loading. The opposite is
also true, which is why this circuit should NEVER be used with
loads less then 25mA.
- It cannot absorb negative load
transistors only conduct in one direction - make sure your circuit
will not generate negative current surges.
- Keep layout compact
- This is a very fast circuit. It has behaved well for me so far,
but long traces at sensitive nodes may encourage it to do things
it ordinarily wouldn't.
- It is not a fixed-voltage regulator
- the output just lags the input by several seconds
- The output voltage will track the input voltage over time - this
can be to your advantage. If your rails can vary by several volts,
you won't need the full voltage headroom you would need for a
fixed-voltage regulator. The Kmultiplier will always "relax" to
1.8V voltage drop between input and output. However if your
circuit needs a precise and regulated supply voltage, this circuit
may not be for you.
Initially PCBs were provided by a member
of DIYAudio who created his own and put them up online. However it was
discovered these PCBs had a faulty grounding layout resulting in
oscillation. It was then that I decided it would be a good time to
release my own PCBs:
- How do I know when it is working
- A very fine balance is required to maintain the high input
isolation. Therefore if anything is wrong, filtering will be
impaired. To verify that you Kmultiplier is working right, follow
- Turn on your Kmultiplier and have an AC voltmeter at hand.
Short the probes to make sure it can read below 1mVAC.
- Measure and record the input AC voltage and the output AC
- Divide the measured output by the input. Make sure this
matches the specified input isolation.
- The LED should flash when you flip the power switch.
- If the LED is emitting ANY light at all during operation, it
means your Kmultiplier is struggling and failing to meet the
current demand, or that there is a fault.
- The voltage drop roughly corresponds to 3 diode junctions.
Measure the DC voltage between the input and output of your
Kmultiplier. It should be within .15V of the specified voltage
- Isolating the fault
- Voltage drop too high
- Measure the voltage across R2. If it is over 80mV, you're
drawing too much current or Q1 is faulty possibly from
overcurrent or a backwards discharge through the BE junction.
C1 could also be faulty due to aging or exposure to heat over
- Voltage drop too low
- If voltage drop is less than a diode (.6V) Q2 is faulty from
overcurrent, possibly inrush. Rarely, if that is not the
problem, D4 may be shorted.
- LED does not flash during turn-on
- Check your input voltage. Most likely a failure in another
part of the circuit has blown the LED. This will not change
the troubleshooting process.
- Getting help with troubleshooting
you want to change something, beware that it may change troubleshooting
procedures and design considerations. That said, if you are confident
you do not need guidance for your application, here are some ideas and
helpful information. Also, discuss your modifications with us in the Kmultiplier
- Decreasing voltage drop
- One reason people use C-multipliers is because they can tolerate
low input voltages. You can decrease the voltage drop of the
Kmultiplier by taking diodes out of the diode string D1. Beware
however each time you do this you decrease the ripple tolerance by
- Input ripple considerations
- If you are increasing voltage drop in order to have more ripple
tolerance, pay attention to the LED breakover voltage. If you
expect to have more ripple than the specified tolerance for the
original circuit, then upgrade to a green LED instead, or a string
of red LEDs. Otherwise ripple will intermittently turn on the LED
and ruin input isolation.
- The RC time constant will determine
how closely it tracks the input voltage
- For better filtering you may try to increase the RC time
constant, but beware that the "stiffer" the filter, the more
likely that rail sag and power demands will saturate it and
possibly cause glitches.
Other adaptions of the Kmultiplier
version is good for the frontend of very high-power amps with 100V
rails, or any application where you need more than 45V output. It can be
used at any rail voltage, regardless of the transistors' individual
voltage limits, as long as the capacitors are up to it. The only
difference is the startup is immediate rather than delayed, and it needs
a lot of diodes.
Is there a Kmultiplier I can use for a
Kmultiplier for higher currents is not so simple. An increased number of
active devices is required, and new feedback loops must be added. This
creates a pandora's box of new difficulties which are not in the
original design simply because of its simplicity. A more powerful
version needs compensations and very careful dimensioning to achieve the
benefits of low voltage drop, low output impedance and compatibility
with well-decoupled designs. The resulting circuit is not so elegant in
its presentation or its performance, but I think it can be done, and I
may have done it. I will link to it tentatively.
Theory of Operation
design of this circuit begun when I was thinking about the capacitance
multiplier circuit block, shown below. The C-multiplier is such a
useful, underused circuit. It can replace banks of caps, given enough
voltage headroom. Furthermore its input isolation can be a big bonus for
RF filtering provided you select transistors carefully. However it
seemed to me no one had thought about this circuit for decades.
Relegated to ancient history, no one seemed to grasp it's potential when
revamped with modern transistors and design expertise. Here is the whole
is called the capacitance multiplier because, (according to theory) it
appears to the load as if C1 has been multiplied by the Hfe of Q1. This
particular transistor has an Hfe of 150 or so, which means our load sees
a supply capacitance of about 1500uF.
Those who have gotten this far probably understand that the reality is
less pretty. After all, the BE junction of Q1 acts like a silicon diode
in series with the load. This means the output impedance of this filter
circuit is very high, and very nonlinear. The impedance of general
purpose silicon follows the rule R=.033/Id, where R is the small-signal
resistance of the junction and Id is it's forward bias current in the
given application. So if our load draws about 40mA, then our filter has
an output impedance of tentatively .825 ohms. This is abysmal.
As seen by the load, R1 is also divided by the Hfe of Q1, and this is in
series with the "diodic" output impedance - 825mR+(100R/150Hfe)=1.492R.
Even worse. But this is followed by a sigh of relief when we realize
that at AC the transistor's base sees a short through C1, returning the
output impedance to 825mR.
Even so the nearly doubled output resistance at DC looms over us. Lets set up a
comparison to give a sense of reality and scale to these figures. This
circuit tries to emulate a 1500uF capacitor. A standard electrolytic
capacitor in this range has around 50mR or .05 ohms. Furthermore, the
transistor only conducts one way, unlike the capacitor which can absorb
negative current surges. So as you can see, the circuit does not really
compare to a real capacitor. They are so different they cannot be
treated like equivalents. The drawbacks are listed as follows:
- High output impedance
- potentially much more than an equivalent electrolytic and even
the rectifier and transformer winding.
- Early effect causes Vbe to modulate with Vce, injecting wideband
input noise into the output. Transistor selection can reduce this,
especially at lower output currents.
- No negative surge tolerance
- The transistor only conducts current
aside, the circuit still has one considerable benefit over a bare 1500uF
electrolytic. This is ripple rejection and input isolation. As Q1 is in
the emitter follower configuration, the emitter follows the base
voltage, and the base is fed by an RC lowpass filter of
100R*100uF. We don't get the benefit of this RC arrangement with
just a 1500uF capacitor - where the only R is that of the rectifier
diodes and the transformer winding. The input isolation is limited only
by the RC corner frequency and transistor leakage. Depending on the
transistor, you may expect AC input rejection from 40-70db. This is
where transistor selection makes all the difference. I won't go into
detail on all the ways to improve this dinosaur, but here are a number
of ways for you to consider if you don't really need the performance
that can be gained from an extra transistor:
- Use a second-order RC filter
- Much improves isolation near the corner frequency, and at higher
frequencies up to the leakage limit.
- Use a diode string or LED in place of the
- This will make turn-on instant and dynamically adjust resistance
to keep Vcb equal to the diode breakover. But watch the input
ripple and your voltage drop.
- Use an FET or MOSFET
- This lets you make the resistor exceedingly large. What you gain
in corner frequency you may lose in leakage, voltage drop, and
output impedance. Perhaps this concept is more applicable to
active audio filters.
this point there are many, many things we could try to tailor the
performance in many directions. Of these, the options adding another
active device tend to become a bit less flexible. If we replace Q1 with
a Darlington pair for instance (diagram below), you will need to draw
enough current at all times to keep the driver transistor on. An extra
diode drop is added, but possibly offset by a lower R1 voltage drop.
Even so, the performance gains can be dramatic. Due to the greatly
decreased base current, we can increase R1 by several times. This allows
output filtering to the subsonics, or alternatively less resistive
output impedance at DC. However AC output impedance can be made worse.
Say for instance our driver transistor is biased at 2mA and our output
transistor has an Hfe of 100. The load draws 102mA. Following the diodic
output impedance rule, Q1 defines most of the output impedance at 330mR.
It's base current is 100mA/100, 1mA. The diodic resistance of Q2's
emitter is divided by the output's Hfe like in the original
C-multiplier, and comes to 165mR. So the total output impedance,
neglecting R1, is 495mR. Often times designers neglect to give the
driver any bias current at all except the base current of the
output. Because the output's base current rises proportionally with load
current, and the diodic emitter resistance decreases proportionally with
emitter current, the net result is that proportions cancel, and the
Darlington output resistance gains the nonlinearity of 2 diodes in
series - 660mR. Neat, right? Of course, you had better decouple the
supplies well, because any fast load signals will saturate and pump the
driver transistor and result in nasty glitching.
the Darlington C-multiplier still leaves us wanting more. Many designers
don't feel like pushing the limit - the C-multiplier was never the
Rolls Royce of supply solutions anyway. Why not just use an LM7812? But
because of reasons mentioned at the beginning of this page, even that is
not a satisfying option. Is there a middle ground between simplicity,
expediency and performance?
Most designers already know about the benefits of a CFP over a
Darlington, even though few seem to have thought to apply it to a
C-multiplier. The CFP has higher transconductance in common emitter
form, which translates to lower output impedance in common collector
form. However the general consensus on the CFP from amplifier designers
is that it is unstable and risky. Many early amplifier designs featuring
CFP output stages were found to up and blow up one day for no apparent
reason. Eventually it came out that the cause was that it has a tendency
to oscillate, causing the transistors to dissipate a lot more power than
they should have. For well-trained amplifier designers, the problem is
just a matter of engineering, but the circuit in question must be
measured in the prototype; RF parasitics depend so heavily on wiring
that it is easier just to probe with a signal generator. Truth be told
many designers don't have the background necessary to understand the
I can go into detail on what the problem is in another article, but here
I will discuss the principle of operation.
Here again is the Kmultiplier diagram for you to refer to throughout my
name for the CFP could be the "G-multiplier pair". In essence, the
output conductance is the conductance of Q1 multiplied by the
current gain of the Q2/R1 arrangement. Let's analyze the situation and
get an idea of how this works.
Q1 is biased into
it's most linear range by R1. So Ic(Q1) is roughly .68/47=~15mA. This is
a bit low to accommodate for a nominal max of 5mA Ib(Q2). In the nominal
range of loading Ic(Q1) ranges from 15mA to 20mA. So, once more
following the diode rules, the output resistance of Q1 varies between
2.2R and 1.65R. Now lets include Q2. Lets say our load current is 116mA.
This sets the Ic of Q1 and Q2 to 100mA and 16mA respectively, accounting
for Q2's Hfe of about 100. At 100mA, Q2's Re is about 330mR. For every
1mA of loading, Vbe(Q2) increases 330uV. This increase in voltage across
R1 results in a 7uA increase in it's current. This is added to the
increase in Ib(Q2) of 10uA and we get an increase in Ic(Q1) of 17uA.
17uA across Q2's Re of ~2.2R gives us a final 37uV output drop per 1mA.
37uV/1mA gives us 37mR as the entire arrangement's output impedance.
This is close enough for horseshoes to the measured values.
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