~ Bicycle Dynamos & RIAA Equalisation Amplifiers ~

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 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 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

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 has only a fixed coil of wire and a rotating 'permanent' magnet generating a.c. but the coiled wire has inductance L_D and also a resistance R_D and due to the winding layers 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 not correctly because a voltage source in series with the inductor will give an output at d.c. and not a voltage proportional to frequency ~ The schematic on the right is more representative of a dynamo or magnetic pick–up cartridge where the inductor L_D is also the generator but neither indicate if the magnet is the fixed or moving part

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 also some parallel capacitive reactance X_C but they are or 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 due to rotation speed change

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 that 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 dissipate 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 ~ the value 0.159 [1/2π] crops up a lot when 'normalising' reactive circuits ~ 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 the current through a resistor are always in phase ~ 1V peak [Vpk] across the resistor produces 1Apk 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

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 [or I×V] is generated between the 5 zero crossing points but unlike the resistors real power half of it is negative [generated by the inductor itself] so the average power per cycle in the inductor is zero but for a part of a cycle could be very real

If an inductor circuit is suddenly broken ~ especially when the current is at a peak ~ the rate of change of current falling to zero will be much greater than at the sine wave zero crossing points ~ Often so great that V_L=−L(∂I/∂t) now produces a back emf greater than the normal peak voltage and we may see [or feel or hear] an arc at the disconnection point

If the resistive power is real the inductive or any 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

An ideal inductor will only have inductance no resistance or capacitance ~ Capacitors can be manufactured more ideal than inductors with very low losses and high insulation resistance ~ Practical inductors will have winding resistance and capacitance plus losses due to magnetic field leakage and or hysteresis if cores are used

Inductors change their [not desired] resistance and their [required] inductance as temperature changes ~ They are susceptible to magnetic fields and electro-magnetic fields [EM or Radio waves] and require special housing if used in low signal level and audio circuits ~ Capacitors can use the outside foil of winding as a screen

At any frequency [including zero Hz d.c.] an ideal reactance will 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 [never a real or practical] inductor or capacitor both of which are never [practical ]

Any deviation from an ideal reactance can be accounted for by including additional capacitance or inductance or resistance in the component model ~ Dielectric and other losses in a capacitor can be represented by series and or parallel resistors and sometimes by additional C–R paths to model the effect of losses with frequency or time

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 temperature and with frequency due to skin effect

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 a vector 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 or C and R 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

Moving the X_L vector to the right to form a 90˚ triangle and applying some trigonometry|Z|∡Θ can also be described as |Z|CosΘ+|Z|SinΘ which is normally written as |Z|(CosΘ+JSinΘ) and known as the 'rectangular' form of the 'polar' vector |Z|∡Θ where +j or −j indicates which quadrant ~ Single L–R or C–R circuit phase cannot exceed 90˚

An impedance diagram is a specific form of Phasor Diagram where it is usual to show resistive vectors R or V_R or I_R along the positive x axis as a 0˚ phase reference [because resistor V and I are in phase] and reactive vectors ±90˚ ~ Impedance values Z occupy the space in one of the right-hand side quadrants

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 Z²=X_L²+R² 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 the j indicates this 90˚ relationship

Z_L=R₁+jX_L is an unambiguous form to define a resistor and inductor in series ~ For a capacitor and resistor in series Z_C=R₂−jX_C ~ The terms R₁+jX_L and R₂−jX_C are known as complex numbers because they require 2 parts to define both the amplitude and the phase with time or frequency

The complex impedances R₁+jX_L and R₂−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=(R₁+R₂)+(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 (R₁+R₂)

Here 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 ~ For a while at least

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 an exponential curve gives the same curve ~ The rate of rate of change of current is the same as the rate of change of current ~ If ∂I/∂t is made to follow the initial t0 rate we can simply use I/t

If the rate of change of current could be kept linear at value V_IN/R/t until V_OUT=V_IN and I limits at the value V_IN/R [as shown by the dotted line] the time now 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 time constant where e⁻¹=0.368

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 stopping the current and losing Φ often with a large spark and a big bang [fact not theory]

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 L–R circuit so τ = L/R seconds

Similarly for any C–R 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 d.c. input voltage ~ They will also have the same frequency response or transfer function for a.c. provided the time constants are the same ~ The resistor R can be any value and the voltage transfer function [Output/Input] is fully defined by time constants L/R or CR alone

Leonhard Euler who in the 1700s created the concept of √−1 gave it the symbol i but j is often used ~ He also introduced the symbol for π and many others and did mathematical studies of music and sounds but best of all he proved that [in terms used here]  |Z|∡Θ = |Z|(CosΘ+JSinΘ) = |Z|e^jΘ which neatly links all the above methods and some

Whatever formula is used for the transfer function of C–R or L–R circuits 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 in practical circuits by values of C or L and the 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 C–R circuits and 2 L–R 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 C–R and L–R but they need finite source and or load R to work against

The methods above for describing C–R and L–R 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 C–R and L–R networks as frequency changes and accepting the notion of j 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 [ƒ] and constants CR or L/R ~ From the impedance graph above R+jX_L or R−jX_C is the complex impedance Z looking into each series network and √R²+X² is the magnitude or real part of Z expressed |Z|

Considering the 2 low pass filters where H(s) = 1/(1+s) 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| which is V_OUT/V_IN so we can plot the amplitude response [A] against frequency [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)

RIAA Equalisation aka BS 1928

The Recording Industry Association of America [RIAA] was formed 1952 to oversee payment of copyright fees for music artists and around 1954 along with other international 'associations' they also set a new fixed definition for the Equalisation required to record sound on the emerging Fine or microgroove gramophone discs

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 ~ The equivalent British Standard BS 1928 or RIAA vinyl record specification

The RIAA or BS1925 replay Equalisation [EQ] 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 functions are multiplied like any other numbers to give an accurately defined replay transfer function

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

The engineer way to present transfer functions is a graph of amplitude [A] and maybe phase [P] against frequency [ƒ] ~ 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 τ₃ τ₂ and τ₁ in frequency order with τ₃ assigned to the lowest frequency but it can be seen that swapping τ₃ and τ₁ makes no difference to the result ~ The standard [specification] for Vinyl disc playback or replay and record only has only 3 time constants and is only defined between 20Hz and 20kHz

τ₃=3180µs ≈50.05Hz    τ₂=318µs ≈500.5Hz    τ₁=75us ≈2122Hz

The magnetic cartridge RIAA replay graph above shows the amplitude response A in dB against logarithmic frequency for the RIAA curve as defined by its 3 time constants ~ The 3180µs pole corrects from 50Hz upward for the signal from a magnetic pickup which like a lightly loaded 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 simple EF86 valve phono stage ~ They may still need the other time constants provided by the reduced ceramic cartridge RIAA replay EQ

A magnetic cartridge may be a moving magnet or moving coil or moving iron but whatever type it is when correctly loaded it should have an output that increases at 6dB/octave [6dB/oct] 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 EQ graph above is also the response of the output from a magnetic cartridge as well as 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 but however your vinyl records are cut that's what you get

Recording and Playback Velocity and Amplitude

If a level frequency signal is fed to a magnetic cutting head the amplitude of the groove will reduce 6dB/oct due to the cutter impedance increasing proportionally with frequency ~ This makes the maximum velocity of the cutter constant as indicated below by the same slope of the zero crossing point tangents ~ This is referred to as Constant Velocity

Cutting head velocity has a 'slew rate' expressed in cm/s which is limited by the mechanics of the head and the mastering material used and which varies from outer to inner tracks due to the change of linear velocity ~ As stated above RIAA Record EQ gives 2 sections of constant amplitude cut either side of the audio band centre

A 12" Long Playing [LP] microgroove disc turning at 33⅓ rpm has a linear velocity of about 0.5m/s [50cm/s] at the outside edge and at a squeeze fits an average 100 grooves/cm when using variable pitch spacing ~ The highest obtainable recorded velocity cannot exceed the linear velocity due to the flat face and 45˚ back angle of the cutting tool

With the 12.5dB step the maximum lateral velocity at 8kHz is ≈19µm/62.5µs×π/2 =0.477m/s which is just about recordable at the edge of a 12" 33⅓ rpm vinyl record ~ Between 2kHz and 8kHz it is possible to have higher than expected levels without distortion and nowadays with better variable pitch more bass output is possible so we get more even if not required

This is the way gramophone record reproduction is and always has been ~ Unlike CD players and other digital media the gramophone recording process relies on the energy distribution of the music which should be more than 30dB lower at 20kHz than at 1kHz even for music made nowadays and much lower relative to the bass on some recordings

Vinyl test discs like TCS101 [Stereo constant Frequency bands from EMI] have a 0dB reference of 1cm/s rms at 1kHz which would be ≈5cm/s rms at 20kHz but they record tones above 10kHz 6dB lower ~ Commercial test discs like HFS69 use 5cm/s at 1kHz and state for their 300Hz tracking tests figures like +15dB ref. 1.12x10^-3 cm peak which would be an excursion of 63µm presumably only in one direction due to the wording

What is cut on your vinyl record is what you get ~ It is what the artist and or the producers or cutting engineer decided 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 we can do is get the replay equalisation and the low noise amplification correct

Here is yet another graph to show the 3 RIAA replay time constants separately or in the combination τ₁+ τ₂ as 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      τ₃ only      τ₁+τ₂ only      τ₁τ₂τ₃      RIAA = τ₂/τ₁τ₃

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

During the 1970s a.c. coupling was used between phono stage and pre–amp and power amps so several high pass filters already existed in many Hi–Fi systems and in 2009 the 7950µs high pass pole was removed ~ More aggressive rumble filters are often built into phono stages but they should not be considered when calculating replay EQ [Ref.10]

Another 'amendment' that crept into RIAA amplifier folklore due to the late Allen Wright [Ref.6] and some internet wild fires is an additional pole at 3.18µs [50.05kHz] which appears to fit 'numerically' with the other RIAA time constants but is not required as it corrects for an 'incorrect' high frequency roll off for Neumann lath cutter heads

Even if some record cutting lathes have a pole above 20kHz [which most do] attempting to correct for it at replay is both restrictive and difficult and a waste of time ~ The cutting head output falls above 20kHz due to losses and there is often a formal pole somewhere beyond 40kHz which may be 2nd order [12dB/oct] or higher to prevent cutter meltdown

Calculating R & C Values for  RIAA Equalisation

In the past Analogue Radio and TV broadcasters placed the complexity of their systems at the studio and transmitter such that consumer receivers could be made easily and repeatable at low cost ~ The reproduction of music was intended to be similar and the equipment for vinyl discs would use only 2 R and 2 C [2CR] for RIAA equalisation

That was the plan and correct application of the chosen replay Time Constants [TC] was not difficult for manufacturers who followed the rules ~ Like QUAD and LEAK and Radford in the UK who had switched EQ for RIAA and earlier discs [and Tape Heads] that used the same input amplifier which was often a single pentode valve

Most early gramophone designs used 2 terminal 2CR Lumped Networks in a Negative Feedback [NFB] Loop around the single valve ~ usually direct from the anode back to the grid ~ with a series input resistor for the required load and gain determined by the network impedance ~ The QUAD QC22 circuit is a good example

Not long after the 1955 publication of the British 'RIAA standard' BS 1928:1955 an article by J. D. Smith appeared in Wireless World [WW] magazine suggesting that the application of 2CR replay EQ ~ which was intended to be simple ~ was being misunderstood and misquoted by Numerous writers and he did the same

In January 1957 W. H. Livy of EMI Studios London replied by letters WW to the article and J. D. Smith responded ~ Later in 1980 when I read the dialogue I agreed with Livy who after-all was making vinyl records and the equipment used ~ It prompted me to calculate the 4th network using 2CR and present the results simpler [ref.11]

In the early 1980s I was working for a small [only 2 TV channels] British broadcaster and had access to a HP85 which could easily 'do the math' and print results which gave three 2 terminal networks by Livy and the 4th 2 terminal 2CR plus the two 4 terminal 2CR networks that can be scaled for any impedance  ~ When the HP85 was available

Later in 1986 I was issued a PSION organiser and I rewrote the RIAA programs in OPL in the small 16×2 character display on long bus rides in & out of London ~ I also wrote some engineering utilities and other programs ~ And since 2001 html versions available here with some changes to make choosing components simpler

Changing or removing R₀ will not affect the RIAA EQ due to N but is not an option with this topology as it puts the cartridge output e_i into a virtual earth but then the Lipschitz paper never considers that phono cartridges require specific loading to work correctly ~ For a load of R₀ ≈47kΩ the d.c. impedance of N would be 1.5MΩ for a 30dB gain

The resistor R₃ does affect the EQ as shown at ω₆ and even if not fitted the output impedance of the non specified amplifier will affect the EQ ~ Active RIAA is a passive network spoiled by feedback ~ ω₂ due to C₀ is included for the IEC amendment 7950µs and this along with the vague zero ω₆ was enough for me to question the rest of the document

It is clear Stanley Lipschitz is a mathematician from the Layout and Introduction of the draft paper and his use of X for poles and O for zeros in his diagrams which use piecewise straight lines with no specific scales but we can assume the slopes are 6dB/oct ~ I like this simple presentation and have often used it myself and I appreciate the effort ~ however:

What I don't like about the paper are the Abstract / Introduction which states Most current disc preamplifiers have audibly inaccurate RIAA equalization. . . due in part to the perpetuation in print of incorrect formulae for the design of the RIAA equalization networks but the work by RCA and Livy at EMI and others in the 1950s [ Ref.2 ] is not mentioned

The AES is a closed shop and non members have to pay to see articles published in their journals ~ This is reasonable but greatly restricts expanding knowledge and receiving valid feedback from outside the box about questionable articles and audio innovations so I have to agree with Grouch Marx ~ But luckily not all members agree with each other

The Stanley P. Lipschitz Published paper [Ref.10] lists the QUAD 33 pre–amplifier along with 'Distortion in low–noise amplifiers ~ Eric F. Taylor' WW Aug 1977 among references 19 to 29 which he states are good design and also lists 1 to 18 as those with 3 major errors he defines as:

1) Incorrect design equations for the calculation of resistor and capacitor values ~ Use my online calculators and adjust only one component to allow for impedances either side of the RIAA network as the QUAD 33 does

2) Failure to take into account the fact that there is an additional high–frequency comer in the response of an equalized non-inverting amplifier stage ~ Don't use this topology or use an inverting amplifier with shunt NFB plus an input buffer and low R values if worried about noise ~ Or better still no networks in the NFB loop [Passive RIAA]

3) Failure to correctly take into account the limited loop gain available from the amplifier circuit ~ Take it into account ~ A simple 2 transistor amplifier is good enough for magnetic cartridge output to line level ~ a third stage may help which could be an output buffer ~ No networks in a NFB loop reduces requirement for GBW and output drive into low loads

With the introduction of better op–amps things should have become simpler but then followed changes back to valve discrete and balanced amplifiers using valves and transistors and distributed time constants plus additional poles and IEC amendment ~ Keep the RIAA network or sections of it separate from the amplifiers

 

Active or Passive RIAA EQ ?
Lumped or distributed Time Constants ?
Op-Amps or Valves or Transistors ?

The circuit above is a direct copy from the National Semiconductor now Texas Instruments [TI] data sheet for their Hi–Fi Audio operational amplifiers ~ the low noise low distortion LME49710 and LME49860 etc. and although it is only offered as a typical application it demonstrates how little thought goes into these 'designs'

It does show however how a good modern RIAA EQ amplifier can be made using op-amps with predictable gain and very low output impedances and high input impedances such that a simple 2 Resistor and 2 Capacitor passive RIAA EQ block can be placed between them without any interaction or signal loss

It looks like the capacitor and resistor values have been carefully crafted to provide the most accurate RIAA EQ possible ~ The resistors are chosen from the E96 series and as stated are 1% tolerance but I have seen a TI application that recommends 0.1%! ~ The capacitor tolerance of 5% puts paid to any precision the circuit offers

26.1kΩ+909Ω =27.009kΩ and 3.83kΩ+100Ω =3.93kΩ so why not use single E24 series 1% values of 27kΩ and 3.9kΩ ? ~ Calculated using 27kΩ the capacitor 47nF∥33nF should be 81nF not 80nF so use 68nF∥13nF or 51nF∥30nF ~ 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 are better capacitors for this application

This circuit layout with all 3 RIAA time constants 'lumped' in a passive equaliser block between 2 op-amp stages has been used for so many 'boys own book' and Hi–Fi magazine articles but unfortunately its simplicity is often ruined ~ A good example how not to make a phono pre–amp using this method was published by Hi-Fi World

The RIAA–1 topology using standard E12 values [E24 1% in practice] gives a more accurate RIAA equalisation than the Texas Instruments design which has a peak–peak deviation of 0.16dB using perfect component values ~ The age old standard values of 47k 6k8 16n and 47n have a peak–peak deviation from RIAA of only 0.05dB

This circuits Passive Network RIAA–1 is a higher impedance than the TI circuit but this does not affect the noise performance which is dominated by the source S/N and IC1 R4 R5 noise voltage ~ Both circuits have similar overall d.c. 0Hz gain which is about 500x or a 3mV cartridge input gives an RIAA EQ output of about 150mV

The open loop gain A₀ and GBW of the LME49710 enables the gain A of each stage to be increased without affecting the S/N significantly ~ 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 but rather than use coupling capacitors which would also require additional resistors for d.c. biasing it is possible to place capacitors in series with R4 or R6 or both ~ The capacitor 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 that may not be appreciated by some critics even though it keeps the through signal path d.c. coupled and the input offset voltages of the op-amps are now amplified only 1x not >500x

If the amplifier impedances either side of the lumped RIAA block are not zero output and/or infinite input which is what you will find in practice ~ especially when using discrete amplifiers ~ allowance can be made for R_L by making the value of R1∥RL the calculated value of R1 as shown here [Valid for 2&4 terminal RIAA–1&2 networks]

The output [source] impedance of the first stage amplifier [Rs] is in series with R1 so can be incorporated into the RIAA network as R1=R1[calculated]–Rs ~ And incorporating RL of the next stage a single new value of R1[calculated]=(R1+Rs)∥RL will give correct EQ for the 4 terminal topologies of RIAA–1 and RIAA–2

One of the things I fuse the RIAA calculators for is quickly checking published phono amplifier designs ~ which despite Ref.2 and the Lipschitz paper and the expert books ~ still have errors ~ Some expert authors do not give tables or calculations used in their RIAA amplifiers often claiming its too complicated to explain

Electronics for Vinyl by Douglas Self gives precise component values like 344.7kΩ and 9.132nF for his lumped 'Configuration A' topology [RIAA–3] but then shows circuit Figure 10.11 with R5=1.8MΩ which is more than twice what it should be plus the series NFB means the response requires a 4th gain dependant time constant

You may often see RIAA networks with multiple parallel and series components to make 'precise values' that don’t fit the RIAA calculation but have been 'eased' because they are 2 terminal networks in feedback loops where the impedances either side are not suitable and/or cannot be incorporated into the network as RL and Rs above

Aside from problems where the amplifier output impedance is not low enough and negative feedback is developed across say a 1kΩ or greater resistor ~ the use of a 2 terminal RIAA network in a feedback loop means that the gain reduction limits at high frequency at 0dB [1x] often requiring an additional CR correction at the output

For the above reasons and the fact that a high gain amplifier negative feedback network with a 40dB slope just does not sound correct and is often the reason why small scratches on a disc appear 'bigger' than they should is why I prefer passive EQ but if you feel different please do hesitate and do not let me know

One old commercial design that used negative feedback around a 2 transistor amplifier similar to Douglas Self’s and got it right was the QUAD 33 which used a 2 terminal 2CR network [RIAA–2] where the bias resistors form part of the network so R303 & 304 appear as R3=101kΩ for calculation and C103 and 104 are a custom 29nF

While writing these pages I sometimes check to see if the information I intend to add is not available better elsewhere on the internet and I often find some classic misleading and annoying statements like: 'An LCR RIAA network has to be used for passive EQ because the common CR type can only be used in a feedback loop'

It is true that networks type RIAA–3 & RIAA–4 cannot be used for a passive circuit like the TI application above placed between 2 amplifier stages but all 4 RIAA CR lumped network topologies can be used in a passive non feedback form if they are used as the load of a high output impedance 'transconductance' amplifier

Using a current source as a valve anode load with all the EQ block returned to ground offers little or no advantage and would introduce semiconductors and additional shot noise ~ Because another stage may be required before this valve EQ stage for best S/N this may lead to the conclusion that separate time constants between gain stages would be simpler?

Several stages are often required to amplify the small signal levels from magnetic cartridges and the RIAA TCs [CR] could be split across them but each stage has to provide correct gain and loading for each TC ~ With a single EQ block on the 2nd stage the 1st stage can be made with a 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 high 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 0Hz gain is only 25.7dB

Looking back at the RIAA replay transfer function ~ If the gain at 0Hz [d.c.] is ≈25.7dB the gain at 1kHz will be ≈5.8dB so a magnetic pick-up with output of 5mV@1kHz@5cm/s will give a flat equalised output of about 9.7mV@5cm/s ~ About 29.353dB [29.353×] gain is needed before and maybe after this passive network stage

Taking the ECC81 to its max 550V HT supply at 1mA with a 450k R1 load so V_a is still about 100V the effective R1 will be ≈99kΩ so C1≈7.5nF C2≈22nF R2=14.4k ~ This higher impedance network gives ≈2× more gain but the shot noise of the valve will also be amplified so the S/N may not be any better for the 32dB gain

A pentode naturally provides a higher anode output impedance than a triode but may add more noise ~ Valves like the E810F pentode have very high g_m as pentode or triode connected but r_a ≈42kΩ ~ An E810F could have up-to 40dB gain in the circuit above with R11 reduced and R1 kept close to 47k because r_a' >3MΩ but anode current is now ≈30mA

Whichever valve is used R11 could be replaced with a FET or BJT which then acts as a current source and also provides pre-stage gain driving the cathode ~ This arrangement or making a valve cascode also has the advantage that the Miller capacitor at the input grid is negligible and constant ~ Else with a RIAA network anode load Miller C is variable

More to come ......

High gm variable miller

 

References and further reading:

Ref.1 ~ Peter M. Copeland ~ BBC [Custard Pete] ~ Analogue Sound Restoration

Ref.2 ~ J. D. Smith & W. H. Livy [EMI Studios Abbey Road London] ~ Wireless World Nov 1956 & Jan 1957

Ref.3 ~ Gramophone Turntable Speeds ~ G. F. Sutton [E.M.I. Engineering] ~ Wireless World June 1951

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

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

Ref.6 ~ Allen Wright ~  Secrets of the phono stage [Rumoured to have started the Neumann pole rumour]

Ref.7 ~ Stanley Kelly ~ Stereo Gramophone Pickup [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. Lipschitz ~ On RIAA Equalisation Networks – Draft [ JAES Vole. 27  Published  June 1979]

Ref.11 ~ Keith Snook 1982 ~ RIAA Lumped RIAA equalisation calculations

Ref.12 ~ Keith Snook 1987 ~ RIAA Component calculators and Frequency Response program for Psion Organiser

Ref.13 ~ H. P. Walker ~ Stereo Mixer ~ Wireless World May 1971

Ref.14 ~ H. P. Walker ~ Low-noise Audio Amplifiers ~ Wireless World May 1972 [Parallel or Series NFB ?]

" You call me a fool ~ You say it's a crazy scheme "