Back in the 1970s when I started earning pocket money to buy Vinyl records I had a bicycle that I made from parts of other 'bikes' which I used for my paper round and getting to the main library in the next town

I often rode when it was dark so I fitted a 6 volt dynamo the rear wheel of my bike which powered a red rear light and a dim front one for free ~ No batteries but no light when stationary

No matter how fast I rode or turned the wheel with the bike upside–down the lights would not get any brighter ~ The only way to set the light output was to choose specific wattage 6V bulbs for the front and back

Upside-down and spinning the wheel really fast you could get a shock with no bulbs connected ~ The voltage was far higher than 6V but less than I have experienced since

A bicycle dynamo uses permanent magnets moving relative to a fixed coil of wire to generate a sine wave voltage proportional to the speed of rotation ~ The output from a dynamo is higher than its rated voltage when not loaded but with the correct bulbs attached the light is fairly constant above an initial slow speed because the source impedance is mainly inductive and this impedance increases as the speed or frequency of current increases

Alternators provide a fixed voltage for a wide range of speed and load conditions unlike a dynamo ~ They do not use magnets but have 'field windings' fed by a variable direct current to create a variable magnetic field ~ A voltage feedback regulator changes the field winding current to control the output voltage independent of rotation speed or load

Pictured is a commonly used schematic of a bicycle dynamo with 2 bulbs ~ L_{D} is the inductance of the fixed iron cored coil and is also the source of a.c. voltage ~ R_{D} is the d.c. resistance of the coil winding ~ The ratio of L_{D }to R_{D} is large so the impedance *Z* between *b* and *chassis* is referred to as 'mainly inductive'

The dynamo impedance *Z* is the reactance X_{L} of the inductance L_{D} added to the resistance R_{D} ~ Reactance is the opposition to a rate of change of current through an inductor or capacitor ~ No other components exhibit reactance but all will have an impedance due to elements of L or C like the dynamo or a wire wound resistor

An ideal dynamo should have only a coil of wire generating a.c. but the coiled wire has inductance L_{D} and also has resistance R_{D }and due to the winding it has capacitance across it ~ Knowing the total impedance of what's inside will be useful when analysing the dynamo looking into point *b* relative to *chassis*

The schematic above is often used to demonstrate dynamos and other a.c. generators and magnetic pickup cartridges but it is not correct because a voltage source in series with the inductor gives an output at d.c. and not a voltage proportional to frequency ~ The schematic on the right is more representative of a dynamo or cartridge where the inductor L_{D} is also the generator

A current source operating from d.c. to a.c. placed across the generator inductor gives a more accurate generator model ~ The bulbs are replaced with a single load resistor R and the unavoidable winding capacitance is added across the inductor which is required for magnetic pickup cartridge and magnetic microphone analysis

All permanent magnet generators have a maximum current limit ~ From stationary or zero Hz the voltage developed across L_{D} is now modelled as truly proportional to speed of rotation or frequency ~ As frequency increases there is a point where X_{L }= R_{D }+ R and the current in R is √0.5 x the current limit

The current limit is set by physical properties of the generator like the strength and coupling of the magnets and losses in the magnetic path and the coil winding method ~ The frequency where X_{L }= R_{D }+ R is also the point where the power in R is half the maximum it can be and is the –3dB frequency referred to when describing frequency and filter responses or more generally transfer functions

Standard wirewound resistors have some series inductive reactance X_{L} and to a lesser extent some parallel capacitive reactance X_{C} but they should be mainly resistive ~ The reactive parts of a wirewound resistor or L_{D} in the dynamo do not dissipate any power but they do influence the flow of a.c. as frequency changes

Reactances X_{L} and X_{C} are measured in ohms Ω and like resistors oppose the flow of current but only alternating current ~ The reactive value of X_{L} increases and of X_{C} decreases with frequency ~ X_{L}∝ƒ and X_{C}∝1/ƒ and the actual values at any frequency are given by X_{L} = 2πƒL Ω and X_{C} = 1/2πƒC Ω but these Ωs do not produce any power

The white trace below represents the current flowing in the 1Ω resistor R in series with inductor L that has reactance X_{L} = 1Ω ~ If the fixed frequency were say 1kHz then the inductance must be 1/(2πƒ) = 159µH ~ 159 crops up a lot when 'normalising' reactive circuits to 1 ~ A capacitor with 1Ω reactance at 1kHz has a value of 159µF

The white trace also represents the voltage across the 1Ω resistor because the voltage across and current through a resistor are always in phase ~ 1V peak (pk) across the resistor produces 1A pk through it and the real power in the resistor is 1W peak or 0.5W average ~ Use these links to see I_{R}×V_{R} ~ You can almost feel the heat

The current through the inductor is the same phase as the resistor current ~ Because they are in series ~ but the voltage across the inductor is 90˚ out of phase

The peak (maximum) voltage across the inductor occurs at the zero current crossing points where the rate of change of current is maximum ~ When the inductor voltage is maximum its current is zero and vice versa

When either current or voltage are zero 3 times each cycle there is no power generated ~ In the inductor this occurs 5 times per cycle ~ But what happens between these 5 zero points ?

Inductors oppose the flow of a.c. by generating a 'back emf' which is maximum at the maximum rate of current change [crossing zero] ~ In a dynamo L_{D} generates a rotating magnetic field opposing the fixed magnet and because of this a dynamo with a constant load cannot produce more power beyond a certain speed simply by turning faster even though the higher speed generates a higher voltage [inside the dynamo]

The formula for back emf is V_{L} = –L(∂I/∂t) when the current through the inductor falls the voltage across it rises and multiplying I_{L}×V_{L }at any time we get the instantaneous power in the inductor ~ Power is generated between the 5 zero crossing points but unlike the resistors real power half of it is negative so the average per cycle is zero

If the circuit is suddenly broken ~ especially when the current is at a peak ~ the rate of fall of current to zero will be much greater than at the sine wave zero crossings ~ often so much more that V_{L} = –L(∂I/∂t) now produces a back emf greater than the normal peak voltage and we may see an arc at the disconnection point

If the resistive power is real the inductive or reactive power (half of which is negative) can be considered as apparent or imaginary ~ The current through a capacitor is also 90˚ out of phase with the voltage across it and there are also 5 zero crossings and imaginary reactive power when I_{C}×V_{C} is integrated over a whole number of cycles

Ideal inductors should have only inductance and no resistance or capacitance ~ In practice capacitors can be made more ideal than inductors with very low inductance and losses and very high insulation resistance ~ Practical inductors will have winding resistance and capacitance plus losses due to the magnetic field leaking and the core material

At any frequency [including zero Hz d.c.] an ideal reactance does not dissipate any power ~ This condition for zero power despite current flowing only occurs when the voltage across and current through a component are 90˚ apart and that component will be an ideal [not a real or practical] inductor or capacitor

Any deviation from an ideal reactance of which there are many can be accounted for by including additional reactance and resistance in the component model ~ Dielectric and other losses in a capacitor can be represented by series and or parallel resistors and sometimes by multiple CR paths to model the effect of losses with frequency

The proportionally higher losses in inductors can also be represented by series and parallel resistors ~ The core material where used may have non linear losses due to hysteresis and saturation as flux density changes ~ The coil winding resistance is an obvious loss which also increases with frequency due to skin effect

The R–L potential divider circuit normalised to 1Ω described above or a dynamo or a magnetic pickup can be expressed on a graph where the relationship between R L andR and L are in series so the x axis can indicate the value of R or the voltage across R or the current in the circuit ~ The y axis shows that the inductive reactance or voltage across L is leading the current through 90˚ as in the waveform graph above

We can calculate the voltage V_{IN} across the series R L circuit and the impedance of the circuit ~ In order to have V_{L} leading V_{R} by 90˚ V_{IN} must lead V_{R }by 45˚ and lag V_{L} by 45˚ in this case where R and X_{L }are the same ~ The magnitude of the impedance |*Z|* is given by √R^{2}+X_{L}^{2} and *Z* = |*Z*| ∠Θ

The impedance Z has to be expressed using 2 terms ~ magnitude and phase ~ so *Z* = 1.414Ω ∠45˚ ~ Applying V_{IN }= 1.414Vpk at the frequency where X_{L }=1Ω the input current will be 1Apk and the circuit waveform relationships will look like those shown above with V_{IN} leading V_{R }(and I_{R}) by 45˚ and lagging V_{L} by 45˚

On an impedance diagram X_{L }is strictly X_{L }∠90˚ and X_{C} would be X_{C }∠270˚ or X_{C} ∠–90˚ ~ If we want to determine |Z| ∠Θ for other frequencies or other values of R and L this x y representation is easier than drawing waveforms but X_{L} needs to be calculated for each fixed frequency so its use is limited

The negative x axis indicates a 180˚ phase shift relative to values on the positive x axis ~ We can replace –R by j^{2}R where j = √–1 which Leonhard Euler called an 'imaginary unit' ~ Imaginary power in reactances could only lead to imaginary units but this will allow us to explain them using mathematical formulas

As we have defined j^{2}R = R∠180˚ it is reasonable to define X_{L} ∠90˚ as jX_{L }from which it follows that X_{C} ∠–90˚ is defined as –jX_{C }as shown if you click here ~ click image to revert

The term jX_{L} means that X_{L} is multiplied by j and –jX_{C} that X_{C }is multiplied by –j or j^{3} ~ Although j is an imaginary concept each multiplication by j rotates a vector by 90˚

Above the series L–R potential divider impedance was calculated as *Z* = 1.414Ω ∠45˚ because X_{L} R and Z follow the sides of a right angle triangle where Z^{2} = X_{L}^{2} + R^{2 }and in polar form *|Z|* ∠Θ can be calculated knowing the relationship between X_{L} and R is orthogonal (90˚) ~ In the expression Z = R + jX_{L} ~ j indicates the 90˚ relationship

Z_{L} = R_{1} +jX_{L} is the simplest unambiguous form to define a resistor and inductor in series ~ For a capacitor and resistor in series Z_{C} = R_{2} –jX_{C} ~ The terms R_{1} +jX_{L} and R_{2} –jX_{C} are known as complex numbers because they require 2 parts to define both amplitude and phase with time or frequency

The complex impedances R_{1} +jX_{L} and R_{2} –jX_{C} can be added together to give the impedance of a series RCL circuit ~ The real R values and the imaginary X values are added separately Z=(R_{1}+R_{2})+(jX_{L} –jX_{C}) ~ There will be a frequency where jX_{L} = –jX_{C} and the circuit is said to be resonant and the reactances cancel leaving only (R_{1}+R_{2})

Here and elsewhere on this site the j operator is simply used to indicate multiples of the 90˚ relationship and remind us that X_{C} and X_{L} are resistances that do not dissipate power ~ If a potential divider is made using two identical resistors the output voltage V_{OUT} is 0.5× V_{IN} but if one arm is a reactance equal to R the output is √0.5× V_{IN}

Time is Constant ~ But how we perceive time may Vary

In the formula V_{L}= –L(∂I/∂t) the derivatives ∂ indicate there has to be a rate of change of current I with time t for V_{L} to exist ~ If the inductor were fed with direct current that increased linearly with time the voltage across L would be constant or put another way if a d.c. voltage across L were constant the current through it must be increasing linearly until limited by say a series resistor or it collapses due to a large magnetic field

Configured as shown above the initial rate of change of current through the circuit at switch on [t=0] is _{IN}/R/t_{L}=V_{IN }_{IN}/R/t

As current starts to flow V_{OUT} across R reduces V_{L} and _{L} approaches zero and V_{OUT} approaches V_{IN}

The currents and voltages follow the curves shown and at time interval t1 V_{OUT} is 0.632 of V_{IN} ~ From t1 to t2 V_{OUT} increases 0.632 of its t1 value and from t2 to t3 . . . yeah it's an exponential curve

The natural response of an L↴R circuit to a step change of input is an exponential curve and will be for a long time ~ Differentiating the curve gives the same curve ~ The rate of rate of change of current is the same as the rate of change of current ~ If

When the rate of change of current is kept linear at V_{IN}/R/t until V_{OUT }= V_{IN} and I limits at V_{IN}/R as shown dotted the time taken to reach V_{IN} is known as the LR circuit time constant and is given the Greek letter tau τ which is also know as the exponential decay constant where *e*^{–1} = 0.368

The L↴R circuit [L in series with the input and output across R] is a low pass filter which can also be made with a R↴C circuit [R in series with the input and output across C] ~ In both cases the output will be 0.993V_{IN} after 5τ and for most practical purposes when t>5τ V_{OUT} is considered equal to V_{IN}

Configured as shown above the circuit current at t=0 is V_{IN}/R ~ As the capacitor charges V_{OUT} increases as shown because V_{R} falling reduces the rate of charge current V_{R}/R/t

The currents and voltages follow the curves shown and at time interval t1 V_{OUT} is 0.632 of V_{IN} ~ From t1 to t2 V_{OUT} increases 0.632 of its t1 value and from t2 to t3 . . .

If the charging current were kept constant the capacitor would charge faster as V_{OUT} increases linearly [shown dotted] until V_{OUT} = V_{IN} at time interval 1 and this is the definition of the time constant τ
for a CR circuit

The inductor equivalent of the charge Q = It = CV stored in a capacitor is magnetic flux Φ = Vt = IL but unlike a capacitor we cannot simply disconnect an inductor from a circuit without disrupting the current and losing Φ often with a large spark and a bang

Rearranging Φ = Vt = IL we get t = IL/V and substituting I/V with 1/R we get t = L/R ~ From the definition above this is the time constant for an LR circuit so τ = L/R seconds

Similarly for any CR circuit rearranging Q = It = CV we get t = CV/I and substituting V/I with R we get t = CR and from the definition for the time constant above we have τ = CR seconds

As shown the L↴R and R↴C circuits have the same response to a step change of input voltage ~ They will also have the same frequency response or transfer function provided the time constants are the same ~ The resistor R can be any value and the voltage transfer function [Output/Input] is fully mathematically defined by time constants L/R or CR

When applying formula for the transfer function of CR or LR circuits or networks containing several LC and R it is assumed the input is from a 0Ω source and the output is loaded by ∞Ω ~ Hence the statement above ~ R can be any value ~ But in practice not too high or too low and often dictated by practical values of C or L and source and load impedances

Although the L↴R and R↴C have exactly the same low pass transfer function they appear as different loads to the source and different impedances to the load ~ At d.c. the L↴R circuit is 0Ω from input to output and with our ∞Ω output load the source sees only R as a load ~ the R↴C source sees an open circuit in series with R

There are 2 CR circuits and 2 LR circuits giving 2 high pass filter and 2 low pass filter responses ~ these are passive attenuator circuits where the output cannot be more than the input and the transfer function maximum is 1 ~ There are also 4 Parallel combinations of CR and LR but they need finite source and load R to work against

The methods above for describing CR and LR circuits can be interchanged and this is the subject of some interesting mathematics Ref.8 which shows other ways of describing and plotting transfer functions but the most useful I think is Laplace's s notation where H(s) precisely describes a transfer function in simple terms with s as the frequency x axis

Knowing the relationship between current and voltage in CR and LR networks as frequency changes and accepting the notion of j simply as an indicator that they have a 90˚ phase difference we can use basic potential divider ohms law to derive mathematical expressions for the 4 series transfer functions using s–notation where x axis s = j2πƒ

Selecting the H(s) links above there are 2 low pass and 2 high pass filters which are fully mathematically defined from ƒ = 0Hz to ƒ = ∞Hz using only the variable s and constants CR or L/R ~ From the impedance graph above R+jXConsidering the 2 low pass filters where H(s) = 1/(1+sτ) and where 1+sτ is derived from R+jX_{L} or R+jX_{C} it follows that 1/√(1+sτ)^{2} is the ratio of R/*|Z| *_{OUT}/V_{IN }so we can plot the amplitude response [A] against ƒ ~ Phase is the imaginary part of Z and relative to 0Hz is tan^{-1}(X/R) or using s notation the phase of H(s) is tan^{-1}(sτ)

This 1962 Wireless World article Ref.9 has more about transfer functions and leads into explaining Poles and Zeros with an example of a more complex transfer function [Fig.2 p.226] for a 'fine groove disc play–back equaliser' with 3 time constants or as it is otherwise known the British Standard BS 1928 or RIAA vinyl record replay curve specification

The fine groove or RIAA gramophone equaliser standard in Ref.9 combines 2 low pass filter sections of the form 1/(1+sτ) [poles] and 1 section that can only be called the inverse of a low pass filter (1+sτ) [a zero] ~ The 3 individual transfer function blocks are multiplied like any other numbers to give the accurately defined transfer function

Poles and Zeros are for mathematicians or designing complex control systems only to find the closed loop stability is 'weather dependent' due to many hidden poles and zeros ~ The RIAA transfer function on its own is stable but may not be if used in a feedback loop around an amplifier or if modified to correct for poles and zeros that don't exist

For each low pass filter section the denominator approaches zero as sτ approaches 1 and H(s) approaches infinity but unless negative frequency [or feedback] exists this cannot happen ~ If the H(s) numerator approaches zero the whole function approaches zero hence the term ~ When graphs tend to infinity they can look like circus tent poles hence . . .

The simplest way to present transfer functions is a graph of amplitude and maybe phase against an X axis of frequency ~ If the Y axis is in dBs we can easily display several decades of gain or attenuation and making the X axis the log of frequency keeps the graph narrow and clearly shows linear changes like 20dB/decade as straight sloped lines

I try to keep the suffixes of the 3 RIAA time constants τ_{3} τ_{2} and τ_{1} in frequency order with τ_{3} assigned to the lowest frequency but it can be seen that swapping τ_{3} and τ_{1} makes no difference to the result ~ The standard [specification] for Vinyl disc playback and record only has 3 time constants and is only defined between 20Hz and 20kHz

τ_{3} = 3180µs ≈ 50.05Hz τ_{2 }= 318µs ≈ 500.5Hz τ_{1 }= 75us ≈ 2122Hz

The RIAA Replay graph above shows the amplitude response A in dB against logarithmic frequency for the RIAA Standard curve as defined by its 3 time constants ~ Note this transfer function is for playback equalisation [ EQ ] of the signal from a magnetic pickup cartridge the output of which like an unloaded dynamo is proportional to frequency

Ceramic and crystal cartridges have an output that is proportional to the the groove amplitude so do not require the 3180µs time constant as I mention here with reference to the QUAD QC22 and its EF86 valve phono stage ~ They may still need the other time constants provided by the reduced playback curve Ceramic RIAA graph above

A magnetic cartridge could be moving magnet moving coil or moving iron but whatever type it is when correctly loaded it should have an output that increases at 6dB/octave which is the inverse of the slopes of the RIAA Replay graph between 50Hz to 500Hz and 2122Hz to >100kHz although the standard is only defined between 20Hz and 20kHz

Now may be a good time to read Ref.1 at least from p.100 onward

The RIAA Record graph above shows the response of the output from a magnetic cartridge but is also the EQ curve for the voltage to a record cutting lathe that uses a magnetic cutting head which most do although some are piezo and so use an inverse of the Ceramic RIAA EQ curve ~ However your vinyl records are produced and cut that's what you get

With a Level frequency signal fed to a magnetic cutting head the amplitude of the cut groove will reduce 6dB/octave because the cutter impedance is increasing at that rate ~ This makes the maximum velocity of the cutter constant as indicated by the same slope at the zero crossings pictured below ~ This is referred to as constant Velocity

With RIAA Record EQ applied the frequencies between 50.05Hz to 500.5Hz and 2122Hz to 20kHz sent to a magnetic cutter will give a constant Amplitude cut because the 6dB/octave fall of the cutting head current is negated by the EQ

Below 20Hz and above 20kHz the RIAA EQ standard is not defined and recording studios take precautions to protect their cutter heads and the recording medium ~ sometimes with an additional 6dB/octave reduction in response above 50kHz on some cutting laths

What is cut on your vinyl record is what you get ~ it is what the artist and or the producers or cutting engineer wanted within the limits of the medium and the technology used at the time ~ It may have been recorded or cut directly with valve equipment or transferred from 4 track tape or processed in the most modern digital studio ~ All you can do is get the replay equalisation correct and the required low noise gain

Here is yet another graph to show the 3 RIAA time constants [there are only 3] separately or in the combination τ_{1}+τ_{2} used to EQ crystal or ceramic cartridges ~ Click on the links below to select various curves or download as a layered pdf which I made 1997 and may not work in some browsers but should work in acrobat or other compliant pdf readers

RIAA Replay Gain & Phase t3 only t1 t2 only t1 t2 t3 Riaa = t1/ t3 t2

As stated above the BS 1928/RIAA standard defines the EQ for fine groove records made after 1954 precisely using 3 time constants ~ It was an agreed world wide standard until in 1976 an IEC amendment added a 7950µs pole [albeit with a zero Ref.9 p.229] only to the replay EQ to effect a high pass filter –3dB at 20Hz to reduce rumble

In the 1970s and still today a.c. coupling was used between phono stage and pre-amp and power amps so several high pass filters already existed in most Hi–Fi systems and in 2009 the 7950µs pole was removed ~ Separate more agressive rumble filters are often used in the phono stages but they should not be considered as part of the replay EQ

Another amendment that has crept into RIAA folklore due to the late Alen Wright ref.6 and internet forums was an additional pole at 3.18µs [50.05kHz] which at first sight appears to fit in with the other RIAA time constants but is not required as its intention is to correct for an undefined high frequency roll off in the EQ for Neumann cutter heads

Even if some record cutting lathes have a pole above 20kHz [which most do] attempting to correct for this at replay is both difficult and a waste of time ~ The cutting head output falls naturally above 20kHz due to drive circuitry and mechanical limitations and there is often a formal pole somewhere beyond 40kHz which is 2nd order so falls 12dB/octave

Alen

Under (re)Construction and being added to March 2024 ~ Thanks to Adobe improving their software to the point where it is not just useless but changes stuff that used to work for more than 20 years

Passive RIAA EQ or Active feedback EQ ? Separate time constants or an all in one EQ Block ?

The circuit above is a direct copy from the National SemiconductorIt looks like the capacitor and resistor values have been carefully crafted to provide the most accurate RIAA EQ ~ The resistors are chosen from the E96 series and as stated are 1% tolerance but I have seen an implementation that recommends 0.1%! ~ The capacitor type and tolerance of 5% puts paid to any precision the resistors may give

26.1kΩ+909Ω is 27.009kΩ and 3.83kΩ+100Ω is 3.93kΩ so why not use single E24 series 1% values 27kΩ and 3.9kΩ ? ~ Calculated using 27kΩ the capacitor 47nF||33nF should be 81nF not 80nF so 68nF||13nF or 51nF||30nF ~ The other RIAA capacitor 27nF||4.7nF||500pF should be 27.769nF so rather than 5% polypropylene why not use 27nF||750pF 1% polystyrene which are readily available and I would say are better capacitors for this application

This circuit layout with all 3 RIAA time constants lumped into a passive equaliser block between 2 op-amp stages has been used for so many 'boys own book' and magazine publications ~ A good example how not to make an RIAA pre-amp using this method was published by Hi-Fi World

The same circuit shown above using standard E12 values [E24 1% in practice] gives a more accurate RIAA equalisation than the Texas Instruments "design" with its peak-peak deviation of 0.16dB using perfect components ~ The age old standard values of 47k 6k8 16n and 47n have a peak–peak deviation from perfect RIAA of only 0.05dBThis circuit has a higher impedance passive lumped RIAA than the TI circuit but this does not affect the noise performance which is dominated by the source S/N and op-amp input noise voltage ~ Both circuits as shown have the same overall gain which is about 530x or a 3mV cartridge input gives about 160mV equalised output

The open loop or A_{o} gain and GBW of the LME49710 will allow the gain of each stage to be increased without affecting the S/N greatly ~ If R4 in my circuit were changed to say 100Ω a 3mV cartridge input would give 320mV output with theoretically better S/N ~ Also changing R6 to 1k would give about 0.7V out for a 3mV input

Both circuits are d.c. coupled which is not desirable for a phono stage ~ Rather than use coupling capacitors which would also require additional resistors for d.c. biasing of the op-amps it is possible to place capacitors in series with R4 or R6 or both ~ the values should be calculated to provide a high pass response say -3dB at 20Hz or lower

With capacitors in series with both R6 and R4 the final slope of the the high pass response will be 12dB/oct and will provide a reasonable rumble filter which may not be appreciated by some critics even though it keeps the through signal path d.c. coupled ~ The input offset voltages of the op-amps will only be amplified by 1x so d.c. at the output is near zero

Comparison between the 2 circuits was made with PSpice computer modelling using an Analogue Behavioural Model (ABM) block to provide a perfect inverse RIAA source with a 0Ω output as shown on the rightThe circuits were modelled with various op–amps and the other components shown in the schematic so the impedances around the RIAA EQ section were accounted for

Whether the RIAA EQ is achieved in a single block or in separate sections or is passive or in a feedback loop the source and load impedances will always have an affect on the accuracy of the calculated values

When the source or load impedances around passive RIAA sections or an EQ block ~ as shown above and left ~ are incorporated into the calculation not only is the overall response correct but gain wasted due to coupling can be minimised

The valve circuit on the left uses the same lumped passive EQ as my LME49710 circuit above [RIAA-1 in ref.3] but configured for current drive ~ The output of the triode can be considered as a current source with an internal shunt resistance r_{a} of about 31kΩ for I_{a} = 1mA

The un-bypassed cathode resistor R11 raises r_{a} to r_{a'} ≈ 126kΩ so the resistance affecting the EQ is 126kΩ∥75kΩ which is the required 47kΩ for this lumped RIAA block ~ Any load of the next stage must also be incorporated in the EQ calculation but as the total value of R1 is the only parameter that needs adjustment the calculation is simple and the response of this EQ block predictable

Using a separate current source as the valve anode load with the EQ block returned to ground offers little or no advantage and would introduce semiconductors and or additional noise ~ because some amplification is required before the valve EQ stage for best S/N this may lead to the conclusion that separate time constant gain stages would be easier to use with valves

3 or more stages are often required to amplify the range of signal levels from magnetic cartridges and the RIAA TCs could be split across 2 or 3 of them but each stage has to provide correct loading for the EQ elements ~ When a single EQ block is used on the 2nd stage the 1st stage can be made a very high g_{m} valve with high I_{a} for best S/N

High g_{m} valves tend to have a low r_{a} which is never well defined and varies with the slightest change of heater or HT voltage and with age ~ An un-bypassed cathode resistor gives a higher r_{a'} but at the expense of gain ~ The 1.8kΩ cathode resistor of the ECC81 stage above makes r_{a'} very predictable and stable but the 1kHz gain is only about 6dB

By placing all 3 RIAA time constants in a single EQ block after a flat response high gain 1st stage the construction of a good RIAA pre amplifier is actually easier than using separate EQ sections whether using op-amps or other devices with large amounts of feedback

References and further reading:

ref.1 ~ Peter M. Copeland ~ BBC ~ Analogue Sound Restoration

ref.2 ~ J. D. Smith ~ W.H. Livy (EMI Studios Abbey Road London) ~ Wireless World Nov 1956 & Jan 1957

ref.3 ~ Keith Snook 1982 ~ RIAA Lumped CR equalisation calculations

ref.4 ~ E. A. Faulkner ~ The design of Low-noise audio frequency amplifiers

ref.5 ~ Editor S.W. Amos ~ BBC ~ Radio TV and Audio Reference Book published by Newnes-Butterworth Ltd

ref.6 ~ Allen Wright ~ Secrets of the phono stage

ref.7 ~ Stanley Kelly ~ Stereo Gramophone Pickups (The State of the Art at the end of 1969)

ref.8 ~ Massachusetts Institute of Technology ~ Understanding Poles and Zeros

ref.9 ~ Cathode Ray ~ Transfer Functions & Poles and Zeros ~ Wireless World Apr May 1962

ref.10 ~ Stanley P. Lipshitz ~ On RIAA Equalisation Networks ~ JAES Vol. 27 Iss. 6 pp. 458-481 ~ June 1979

ref.11 ~ Keith Snook 1987 ~RIAA Component calculator and Frequency Response check with Psion Organiser