Passive Filters, Capacitors, Smoothing and Noise in Amps

I want to get to grips with the topic of passive filters – operation, maths and values in amps generally to better read what frequencies are passing to or being blocked between stages.
No doubt I will wonder off at tangents as usual…
I’ll look at

“[fc]…which is the frequency that the filter will attenuate to half its original power.”
to better understand this Cut Off frequency equation (relating to the Time Constant equation, T = RC) for an oscillator in real world scenarios, for both audio signal EQ as well as noise filtering for hum/hash from the mains/rectifier diodes, and radio noise at the grid inputs using grid stopper resistors, for example.
This covers both ends of the human audio frequency spectrum (20-20kHz) that can bring unwanted audio artefacts into an amps audio signal chain. It is possibly relevant at present for some outstanding noise issues I have with both the Maggie and PP18 amps, as I have about a 5 kHz signal superimposed on the audio in the Maggie at a certain volume that I have no idea where it comes from (internal oscillation or external noise?), and I still need to filter or stop the hash peaks in the PP18 OT secondary. Even though my NFB pot is great remedy, it doesn’t treat the cause.

There are four common simple configurations of a capacitor and resistor you may see in a circuit relative to the load they feed.

When the capacitor is in parallel with the load while the resistor is in series with the capacitor and load, this creates a low pass filter.

The first:
low-pass filter is a filter that passes low-frequency signals and attenuates (reduces the amplitude of) signals with frequencies higher than the cutoff frequency.”

The second:

When the resistor is in parallel with the load and the capacitor is in series with the resistor, a high pass filter is created.
high-pass filter (HPF) is an electronic filter that passes high-frequency signals but attenuates (reduces the amplitude of) signals with frequencies lower than the cutoff frequency.”

I visualise these above by thinking that as a capacitor blocks DC – the lowest “frequency” – and passes high frequency for given values of cap and resistor, then where a cap is connected to ground it is a short circuit for the higher frequencies, leaving only lower frequencies to pass to the next stage or load, as in example 1 – the Low Pass filter.
In the High Pass, the DC or LF is blocked from the load leaving only the HF to pass.
So, in general, when you see a capacitor connected to ground it is a “low” pass filter, with the next stage or load, it is a “high” pass filter. How “low” or “high” is defined is relative to what frequencies came before or exist now, and what the component values decide at that point.
The last two examples are combinations of these first two.
This next one is commonly identified after the rectifier diodes in many designs. Their job there though is not to filter audio AC, just have a high enough Time Constant so they discharge minimally within the 100Hz cycle time (positive AND negative unrectified mains cycle period peaks) before the next rectification pulse tops them up again. The Time Constant = R x C in seconds.
The third would be both R and C in parallel to a load:

This would also be a low pass filter as it blocks DC to ground and the lowest frequency passed is decided by the Cut Off value. The differences to understand here is that they are in parallel from a charging point of view, but when the charge source is removed (switched off) and assuming the cap can’t discharge via the load either, it discharges back through the resistor to ground so is in series with the resistor from a discharging point of view, so the TC constant still applies.
Its impedance is minimal for a particular frequency when the impedance of both components is the same, so would be two impedances in parallel:
Z = R || Xc
so ½ of their individual values, like 2 resistors in parallel.
cutoff frequencycorner frequency, or break frequency is a boundary in a system’s frequency response at which energy flowing through the system begins to be reduced (attenuated or reflected) rather than passing through.”
The fourth would be a Band Pass Filter which is a Low and High pass together:
band-pass filter is a device that passes frequencies within a certain range and rejects (attenuates) frequencies outside that range.”
Many other variations and combinations exist of course but those above are the basic building blocks for the principles involved.
“In physicsresonance is the tendency of a system to oscillate with greater amplitude at some frequencies than at others.”
“…characterizes a resonator’s bandwidth relative to its center frequency… The higher the Q, the narrower and ‘sharper’ the peak is.
This band stop (or notch filter if having a very small bandwidth and/or a high Q) is the inverse of a band pass filter so that instead of passing a set band of frequencies and removing all else, it cuts a fixed band with all either side passing through.

Just for awareness, though too high tech for most amps:

Parametric equalizers are multi-band variable equalizers which allow users to control the three primary parameters: amplitudecenter frequency and bandwidth.

Mains Filtering

Note that the principle of mains hum filtering starts at the reservoir capacitor in the DC stage of an amp to remove ripple artefacts, as possibly there are 50Hz and 100Hz generated spikes and harmonics that can pass on or be inductively transferred to the audio signal chain from the initial AC mains rectification process.
Obviously, if these caps filtered 50Hz or 100Hz directly they wouldn’t charge in the first place!
The longer they take to discharge means the higher voltage they hold until next recharge, and the smaller spike they create to possibly become a higher frequency artefact that could pass to the audio chain by other means such as “inductive coupling”. This large Time Constant; T = RC, which generally means “larger capacitor” for a fixed resistor size, has to be balanced by the in rush current they draw upon initial charging at switch on, to not exceed the maximum current rating of the PT secondary, blowing a fuse or causing the Power Transformer to run too hot.
The Time Constant of an RC circuit or the time taken for a capacitor to charge or discharge through a series resistor, applies here to aid understanding, as you can visualise electrons being able to flow on and off a smaller value capacitor more frequently as it takes less electrons to fully charge it, so this happens faster for a given voltage and a higher frequency – so a smaller capacitor appears to “pass” or be more transparent to higher frequencies than lower frequencies. The lowest possible “theoretical” frequency is 0Hz = DC which does not pass via a “perfect” capacitor at all.
0 Hz = 1 /2 Pi x infinite capacitance
The larger the capacitor the lower the frequency it can pass.
Although the following filtering concept and values may not apply in a real OT secondary rectification stage, I am going to use these real circuit numbers to get used to the equation with the calculator, and try and fix the idea in my head in terms of visualising the graph of the low frequency cut off filter they would represent.
If the first rectifier capacitor, usually a 47uF, in parallel with a 220k is looked at in filter terms, it is a VERY low pass filter with a cut off at:

1 / 2 x Pi x 220000 x 0.000 047F = 0.015 Hz Cut Off. All frequencies above this should pass.
For the next cap in the chain – usually a 16uF – this would have a cut off at:
1 / 2 x Pi x 10000 and 0.000 016F = 0.995Hz Cut Off. All frequencies above this should pass.

The next may be a 56k with an 8uF:
1 / 2 x Pi x 56000 and 0.000 008F = 0.355Hz Cut Off. All frequencies above this should pass.

This was a number exercise – don’t confuse it with filtering actual audio frequencies, as the principle in the rectification filter stage here is to get to a point where all the caps hold almost as much DC charge for as long as possible between cycles as the OT secondary peak value and resistor chain can provide. Therefore a large Time Constant (larger cap, larger resistor) would be better in theory for slow discharge, but may cause current in rush current problems for the PT, as it would draw a large current initially to charge from 0V at power on. This is why just putting a large value 100uF cap in the rectifier stage isn’t such an easy solution to reduce ripple in as few stages as possible. It depends on the OT sec current and power rating.

One reservoir capacitor cannot smooth all the ripple voltage (unless it were infinitely large), so we must decide how much HT ripple voltage we can tolerate and choose a capacitor that can achieve it. 
The ripple voltage is expressed as a percentage of the total HT voltage, so a 100Vdc HT with a 10V peak-to-peak ripple ‘riding’ on it has 10% ripple.”

Maggie Ripple:

Above – 50Hz clipped 4V heater signal with 100Hz, 7V DC ripple at A+ for the Maggie. Ripple is twice the heater frequency from full wave, ½ cycle rectification. How much does it discharge by and how quickly?

If the time constant, CR, is large in comparison to the period of the ac waveform, then a reasonably accurate approximation can be made by assuming that the capacitor voltage falls linearly.
This linear drop from a sawtooth waveform is apparent above and can be described by:

“For the rms value of the ripple voltage, the calculation is more involved as the shape of the ripple waveform has a bearing on the result. Assuming a sawtooth waveform is a similar assumption to the ones above and yields the result:[3]


  •  is the ripple factor
  •  is the resistance of the load

For simplicity, I’ll use the common values of for the PT load resistor and reservoir cap again.
Ripple Factor = 1 / 4 x (3 x 100Hz x 0.000 047F x 220 000)^1/2 = 0.017 or 1.7%
As a percentage factor of the source voltage this would be 0.017 x 377V = 6.4V – close…
In reality, in the above scope pic for the Maggie, A+ = 377V, so using Blencowe’s percentage above, ripple noise = 7V/377V x 100% = 1.9 %
The cap voltage has dropped only 1.9% in a 100Hz cycle which is 1/10 second (50Hz = 20ms – remember it). This is close to the equation value considering this scope value is a reading from a full circuit, not just the ripple across a 220K and reservoir cap. This is a very low noise value in Blencowe’s opinion (10% is “good“), but this amp is still quite hashy also – I think because of my messy prototype wiring and poor grounding scheme at the build start allowing lots of unwanted “inductive coupling”.
When (if!) I finally get around to tidying up these amps messy wiring it will be interesting to see how much difference to overall hum noise is made.
The TC for a 220K and 47mF cap = 220000 x 0.000 047 = 10.34 secs which represents the time it would take for the cap to drop by 63% from 377V to 0.63 x 377V to 237V in 10 seconds.
The long 10s time constant relative to the short discharge period before recharging occurs again (every 1/10th sec) ensures the cap remains at a high voltage, as it only dropped by 7V, or 2% in that 1/10th second.
The parallel RC circuit is generally of less interest than the series circuit. This is largely because the output voltage  is equal to the input voltage  — as a result this circuit does not act as a filter on the input signal unless fed by a current source.”

Grid Stoppers

I had another look at the Maggie also with a view to looking at the seemingly high triode2 120k value grid stopper I have in my amp, to learn about radio noise and this resistor at triode2 grid.
This R5 is a 100k in the schematic, but I put 120k in the amp – the closest available I had.

For some reference in real world examples for a triode1 stage – see these amps:
Maggie 68k
PP18 56k
JMP Marshall 68k
Fallen Angel 100k
Fender Tremolux 68k
Fender Champ 68k
Aston 5W 68k
Gibson GA15 33k
Marshall 2060 Lo Input 100k (transistor)
OK, seems 68k is the go generally for 12AX7s so why?
After checking Blencowe’s p87 chapter on the Input Network, I can relay the main reason for use is to low pass filter all wanted audio frequencies into the amp but remove all inaudible frequencies above 20kHz, say. The grid stopper value is calculated by rearranging f = ½ Pi RC:
f = ½ Pi RC becomes R = ½ Pi f C where C is the input capacitance of a 12AX7 grid, at about 100pF.
R = 1 / 0.000 000 0001F x 2 x 3.142 x 20 000Hz = 80 000 ohms
This gives a required grid stopper value of 80k.
Historically, values lower than this are used to keep noise from the resistor itself to a minimum from when noisy carbon composite resistors were used mainly probably, (which should be avoided at the first triode1 input these days with better quality ones available), as in the amp list above.
In Blencowe’s table on p62 there is a factor of ten times more total Johnson and Excess noise in carbon composition resistors than carbon film/metal film, where innate noise is on a scale of micro Volts per Volt. Wire wound types are quieter again by another factor of ten. As stated in Posts in the past, noise is cumulative so I guess an amp design full of carbon composite types over carbon film will be way more than 10 times hissier mathematically – but again don’t forget the ear’s log scale perception – it won’t be too much of an audible increase, but may well be apparent at full volume with no signal?
To stay familiar with the equation, I want to get an idea of the audio range affected by various RC combinations. The grid stopper in series with the triode grid input capacitance forms a low pass filter. Putting the 68K in the equation the 12AX7 triode1 cut off frequency is:
f = ½ Pi RC = 1 / 2 x 3.142 x 68000 x 0.000 000 0001F = 23 405Hz Cut Off (so frequencies HIGHER than this won’t pass into the amplification chain.
So the lower value the grid stopper the lower the innate resistor noise, but the higher the frequency range band is passed into the audio chain before being filtered to ground.
To verify this makes sense, the Gibson 33k should low pass at about twice this again:
f = ½ Pi RC = 1 / 2 x 3.142 x 33000 x 0.000 000 0001F = 48 229Hz.
For the lowest possible grid stopper value before input impedance effects become problematic, a 10k could be used, though the noise level benefit hits a minimum here anyway, the cut off is:
f = ½ Pi RC = 1 / 2 x 3.142 x 10000 x 0.000 000 0001F = 159 154Hz Cut Off (so frequencies BELOW this pass into the amplification chain.

This just happens to be around Longwave AM Radio = 148.5 kHz – 283.5 kHz (LF)

Is it a potential problem?
Well, it seems is but for many reasons, not just due to a frequency range. There are lots of interesting tales of guitar amps picking up radio stations for various reasons here:
Obviously there are many possible factors involved here such as individual amps design, screening, build quality, guitar cable quality and length (an aerial basically), distance from transmitter, station frequency, mains wiring (Earth presence/condition)…but interesting to consider – and funny – unless it happens to you I suppose!
Where does most public, commercial or other likely radio interference source frequencies fit in all this? What other possible noise sources are lurking in the home or intrude somehow? I suppose everyone has heard their mobile phone connecting through a stereo or guitar amp at some point?
Because of the potential for electromagnetic interference between users, the generation of radio waves is strictly regulated by the government in most countries, coordinated by an international standards body called the International Telecommunications Union (ITU). Different parts of the radio spectrum are allocated for different radio transmission technologies and applications.”

“Low frequency or low freq or LF refers to radio frequencies (RF) in the range of 30 kHz–300 kHz. Also known as the kilometre band or kilometre wave as the wavelengths range from one to ten kilometres, the low signal attenuation in this band allows long distance communication. In Europe, and parts of Northern Africa and of Asia, part of the LF spectrum is used for AM broadcasting as the longwave band. In the western hemisphere, its main use is for aircraft beacon, navigation (LORAN), information, and weather systems. Time signal stations MSFHBGDCF77JJYand WWVB are found in this band.”

The closest Longwave Broadcast frequencies are still 3 times higher than the Gibson 33k would possibly pick up in theory, but a 10k grid stop may have issues:

“Very low frequency or VLF refers to radio frequencies (RF) in the range of 3 kHz
to 30 kHz and wavelengths from 10 to 100 kilometres. Since there is not much bandwidth in this band of the radio spectrumaudio (voice) cannot be transmitted, and only low data rate coded signals are used. The VLF band is used for a few radio navigation services, government time radio stations which broadcast time signals to set radio clocks, and for secure military communication. Since VLF waves penetrate about 40 meters into saltwater, they are used for military communication with submarines.”

That was the only comms frequency in the actual audible range I found on WikiP, so, unless you are playing an underwater gig I don’t think you need worry about picking up a nuclear subs chat…
Seriously though, I know I can pick up the beaconing or pulsing mains from my WiFi hub so what frequency is that pulsing at and why? To connect to other devices a WiFi hub generally advertises its existence periodically, like a lighthouse beacon, so it could be that. It may just be the unregulated mains from its cheap PSU also, or both interacting.

Beacon Interval

Range 1 and 65,535 milliseconds. The default value is 100.

The help file says…

  • The Beacon Interval value indicates the frequency interval of the beacon. A beacon is a packet broadcast by the router to synchronize the wireless network. 50 is recommended in poor reception.

100ms is 1/10 sec or 10HZ so inaudible, but 50ms is not at 20Hz, but may not mean there are no harmonics from 100ms that could be audible?
Also, laptop/other PSUs can be really radio noisy through audio gear. I have had major issues with this at DBS through the practise room mixer/P.A. system.
Hang on…! I just read on a radio forum that the 12AX7 has a bandwidth of 10kHz anyway so why would it be a problem picking up 148kHz radio waves?
Can the amp can act as an RF filter in itself and so reproduce just the audio from the carrier as a normal radio does by design, under the right conditions such as long, coiled guitar leads connected?
This dawned on me that that is exactly what an audio amp IS – a 20-20kHz bandpass filter! It’s precisely because it has a bandwidth for audio frequencies that it will be able to filter AM and FM carrier signals if receiving them, leaving just the audio spectrum.
Also, the meaning of Bandwidth relates to a drop in signal voltage by 3dB only (usually) across a specified range of frequencies – not cutting out those frequencies completely.
Every AM and FM modulation produces sidebands added above and below the carrier so there may be a radio sideband in the audio range anyway.
There are further smaller harmonic sidebands at that form a series:
In the case of amplitude and frequency modulation, sidebands occur in pairs on either side of the CARRIER frequency at a distance equal to the modulating frequency.

Now you can see the decaying series of the frequencies on the lower side would eventually fall in the audio range.
How do radio signal voltages compare with guitar input levels? Are they significantly different? It seems they can be very small but still classified below (S1 level) – in the 200 nanoVolt region – but also comparable to guitar levels with the largest being 50mV (S9+60). This is half the test signal I use to simulate a single coil pickup at 100mV using FLS. You would probably have to live next to the radio transmitter to get a signal that big though.

S-points for frequencies below 30 MHz:




Received power
(Zc = 50 Ohm)


-48 dB

0.20 uV

-14 dBuV

790 aW

-121 dBm


-42 dB

0.40 uV

-8 dBuV

3.2 fW

-115 dBm


-36 dB

0.79 uV

-2 dBuV

13 fW

-109 dBm


-30 dB

1.6 uV

4 dBuV

50 fW

-103 dBm


-24 dB

3.2 uV

10 dBuV

200 fW

-97 dBm


-18 dB

6.3 uV

16 dBuV

790 fW

-91 dBm


-12 dB

13 uV

22 dBuV

3.2 pW

-85 dBm


-6 dB

25 uV

28 dBuV

13 pW

-79 dBm


0 dB

50 uV

34 dBuV

50 pW

-73 dBm


10 dB

160 uV

44 dBuV

500 pW

-63 dBm


20 dB

500 uV

54 dBuV

5.0 nW

-53 dBm


30 dB

1.6 mV

64 dBuV

50 nW

-43 dBm


40 dB

5.0 mV

74 dBuV

500 nW

-33 dBm


50 dB

16 mV

84 dBuV

5.0 uW

-23 dBm


60 dB

50 mV

94 dBuV

50 uW

-13 dBm

What can you do about hum noise?
Some ideas below:
For countries with US based/non Earthed, 2 pin only mains systems see this:
What can you do about radio noise?

First, find the source if possible. I turned off my WiFi when the amps were affected close up, within 2m (WiFi at the end of vid) and the pulsing noise went, so I knew the source. I then put the metal RF screens back on the 12AX7s. With the WiFi back on the noise was screened. The vid is here:

I did an experiment with some of my amps and found that plugging in a TV aerial into the Marshall 2060 amplified a voice channel enough (amongst the loud mains and other buzz) to hear some chat:

This was the only amp that did this, probably for many reasons e.g. having a transistor pre amp, and a Hi Z input stage (the Lo input didn’t pick up).
So, for radio station noise, first check you guitar lead is not an aerial. Do you get the station with or without the lead plugged in (but not connected to guitar)? Hi or Lo/Normal input only?
Check you have a good quality screened cable that is not too long. Try a different length etc.
Isolate the problem through elimination of possible causes as in the forums above – starting with the easiest:

  • amp position – is it still a problem in a different room or friends house?
  • different cord, cord length, cord coiled?
  • guitar screening – the silver foil inside the back plate should be wired to the ground of the metal bridge and output jack – the guitar is only Earthed via the amp’s chassis then mains plug when plugged into it. Bad connections anywhere in this chain can prevent noise being Earthed and make the guitar strings an aerial also.
  • mains socket Earth present and good connection to Earth via building wiring. An electrician can check with a PAT (portable appliance) test meter, or a rough method may be using a DDM meter from the Earth pin to a cold mains water pipe. 1 ohm MAX resistance. Be careful and don’t confuse the Earth with the mains live or neutral pins – if in ANY doubt – DONT do it!
  • amp screening – the metal chassis is usually the screen, but the circuit ground to chassis may be bad – get an amp tech to check or use a DDM if you know how to SAFELY.