{"id":4913,"date":"2014-01-12T23:35:52","date_gmt":"2014-01-12T22:35:52","guid":{"rendered":"https:\/\/stevepedwards.today\/quad\/wp\/?p=4913"},"modified":"2019-09-16T02:07:53","modified_gmt":"2019-09-16T01:07:53","slug":"passive-filters-capacitors-smoothing-and-noise-in-amps","status":"publish","type":"post","link":"https:\/\/stevepedwards.today\/ElectronicsStuff\/passive-filters-capacitors-smoothing-and-noise-in-amps\/","title":{"rendered":"Passive Filters, Capacitors, Smoothing and Noise in Amps"},"content":{"rendered":"

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.
\nNo doubt I will wonder off at tangents as usual...
\nI'll look at
\n\"\"
\n\"[fc]...which is the frequency that the filter will attenuate to half its original power.\"<\/span>
\nto 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.
\nThis 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.
\n\"\"
\nThere are four common simple configurations of a capacitor and resistor you may see in a circuit relative to the load they feed.
\nFrom:
\nhttps:\/\/stevepedwards.today\/en.wikiversity.org\/wiki\/RC_Circuit<\/a><\/p>\n

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.
\n<\/span><\/p>\n

The first:
\n<\/strong><\/span><\/p>\n

\"\"
\n<\/span><\/p>\n

https:\/\/en.wikipedia.org\/wiki\/Low-pass_filter<\/a>
\n\"A-\u00a0low-pass filter<\/strong>-\u00a0is a-\u00a0<\/span>filter<\/span>-\u00a0that passes low-<\/span>frequency<\/span>-\u00a0<\/span>signals<\/span>-\u00a0and-\u00a0<\/span>attenuates<\/span>-\u00a0(reduces the-\u00a0<\/span>amplitude<\/span>-\u00a0of) signals with frequencies higher than the-\u00a0<\/span>cutoff frequency<\/span>.\"
\n<\/span><\/span>
\n\"\"<\/p>\n

The second:
\n<\/strong><\/span><\/p>\n

When the resistor is in parallel with the load and the capacitor is in series with the resistor, a high pass filter is created.
\n<\/span><\/p>\n

\"\"
\n<\/span><\/p>\n

https:\/\/en.wikipedia.org\/wiki\/High-pass_filter<\/a>
\n\"A-\u00a0high-pass filter<\/strong>-\u00a0(HPF) is an-\u00a0<\/span>electronic filter<\/span>-\u00a0that passes high-<\/span>frequency<\/span>-\u00a0<\/span>signals<\/span>-\u00a0but-\u00a0<\/span>attenuates<\/span>-\u00a0(reduces the-\u00a0<\/span>amplitude<\/span>-\u00a0of) signals with frequencies lower than the-\u00a0<\/span>cutoff frequency<\/span>.\"<\/span><\/span>
\n\"\"
\nI 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<\/strong> filter.
\nIn the High Pass<\/strong>, the DC or LF is blocked from the load leaving only the HF to pass.
\nSo, 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.
\nThe last two examples are combinations of these first two.
\nThis 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.
\nThe third<\/strong> would be both R and C in parallel to a load:
\n\"\"
\nThis 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<\/strong> 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<\/strong> back through the resistor to ground so is in series<\/em><\/strong> with the resistor from a discharging point of view, so the TC constant still applies.
\nIts impedance is minimal for a particular frequency when the impedance of both components is the same, so would be two impedances in parallel:
\nZ = R || Xc
\nso -\u00bd of their individual values, like 2 resistors in parallel.
\nhttps:\/\/en.wikipedia.org\/wiki\/Cutoff_frequency<\/a>
\n\"a-\u00a0cutoff frequency<\/strong>,-\u00a0corner frequency<\/strong>, or-\u00a0break frequency<\/strong>-\u00a0is a boundary in a system's-\u00a0<\/span>frequency response<\/span>-\u00a0at which energy flowing through the system begins to be reduced (<\/span>attenuated<\/span>-\u00a0or reflected) rather than passing through.\"<\/span><\/span>
\nThe fourth<\/strong> would be a Band Pass Filter which is a Low and High pass together:
\nhttps:\/\/www.electronics-tutorials.ws\/filter\/filter_4.html<\/a>
\n\"\"
\nhttps:\/\/en.wikipedia.org\/wiki\/Band-pass_filter<\/a>
\n\"A-\u00a0band-pass filter<\/strong>-\u00a0is a device that passes-\u00a0<\/span>frequencies<\/span>-\u00a0within a certain range and rejects (<\/span>attenuates<\/span>) frequencies outside that range.\"<\/span><\/span>
\nMany other variations and combinations exist of course but those above are the basic building blocks for the principles involved.
\nhttps:\/\/en.wikipedia.org\/wiki\/Resonant_frequency<\/a>
\n\"In-\u00a0<\/span>physics<\/span>,-\u00a0resonance<\/strong>-\u00a0is the tendency of a system to-\u00a0<\/span>oscillate<\/span>-\u00a0with greater <\/span>amplitude<\/span>-\u00a0at some-\u00a0<\/span>frequencies<\/span>-\u00a0than at others.\"<\/span><\/span>
\n\"\"
\nhttps:\/\/en.wikipedia.org\/wiki\/Q-factor<\/a>
\n\"...characterizes a resonator's-\u00a0<\/span>bandwidth<\/span>-\u00a0relative to its center frequency...<\/span> The higher the Q, the narrower and 'sharper' the peak is.<\/span>\"<\/span><\/span><\/span>
\nhttps:\/\/en.wikipedia.org\/wiki\/Band-stop_filter<\/a>
\nThis 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.
\n\"\"
\nJust for awareness, though too high tech for most amps:
\nhttps:\/\/en.wikipedia.org\/wiki\/Parametric_equalizer#Parametric_equalizer<\/a><\/p>\n

Parametric equalizers are multi-band variable equalizers which allow users to control the three primary parameters:-\u00a0<\/span>amplitude<\/span>,-\u00a0<\/span>center frequency<\/span>-\u00a0and-\u00a0<\/span>bandwidth<\/span>.
\n<\/span><\/span><\/p>\n

\"\"
\nMains Filtering
\n<\/strong><\/span>
\nNote 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.
\nObviously, if these caps filtered 50Hz or 100Hz directly they wouldn't charge in the first place!
\nThe 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.
\nThe 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.
\n0 Hz = 1 \/2 Pi x infinite capacitance
\nThe larger the capacitor the lower the frequency it can pass.
\nAlthough 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.
\nIf 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:
\n\"\"
\n1 \/ 2 x Pi x 220000 x 0.000 047F = 0.015 Hz Cut Off. All frequencies above this should pass.<\/span>
\nFor the next cap in the chain - usually a 16uF - this would have a cut off at:
\n1 \/ 2 x Pi x 10000 and 0.000 016F = 0.995Hz Cut Off. All frequencies above this should pass.
\n<\/span>
\nThe next may be a 56k with an 8uF:
\n1 \/ 2 x Pi x 56000 and 0.000 008F = 0.355Hz Cut Off. All frequencies above this should pass.
\n<\/span>
\nThis 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.
\nhttps:\/\/www.valvewizard.co.uk\/smoothing.html<\/a>
\n\"\"
\n\"One reservoir capacitor cannot smooth-\u00a0all-\u00a0the 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.-\u00a0<\/span>
\nThe 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.\"<\/span><\/span>
\n<\/em>
\nMaggie Ripple:
\n\"\"
\nAbove - 50Hz clipped 4V heater signal with 100Hz, 7V DC ripple at A+ for the Maggie. Ripple is twice the heater frequency from full wave, -\u00bd cycle rectification. How much does it discharge by and how quickly?
\n<\/strong><\/span>
\nhttps:\/\/en.wikipedia.org\/wiki\/Ripple_(electrical)<\/a>
\n<\/strong><\/span>
\nIf the-\u00a0<\/span>time constant<\/span>, 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.<\/span><\/span>
\nThis linear drop from a sawtooth waveform is apparent above and can be described by:<\/p>\n

\"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<\/span>-\u00a0<\/span>sawtooth waveform<\/span>-\u00a0is a similar assumption to the ones above and yields the result:<\/span><\/span>[3]<\/sup><\/span>\"
\n<\/span><\/em><\/p>\n

\"\"
\n<\/span><\/p>\n

where
\n<\/span><\/p>\n