Still Under Construction


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 library in the next town
I often rode when it was dark so I fitted a 6 volt dynamo similar to the one pictured to the rear wheel of the bike that powered a red rear light and dim front one for free No matter how fast I rode or turned the wheel with the bike upsidedown the lights did not appear to get much brighter but upsidedown and spinning the wheel really fast you could get a shock from the dynamo when the lights were not connected I tried various 6V lamps and eventually found a pair that gave a good front and rear light balance but they different wattage 

A bicycle dynamo uses permanent magnets moving relative to a fixed coil of wire to generate an a.c. voltage proportional to the speed of rotation ~ The output from a dynamo will be 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
Car dynamos and alternators provide a fixed voltage for a wide range of load conditons unlike the fixed load of the bicycle dynamo so do not have magnets but use 'field windings' fed by a variable d.c. 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 schematic typical of a bicycle dynamo with 2 lamps connected ~ L_{D} represents the inductance of the fixed iron cored coil which is also the a.c. voltage source ~ R_{D} is the small d.c. resistance of the coil winding ~ The ratio of L_{D }to R_{D} is large hence the impedance Z between b and chassis is referred to as 'mainly inductive'  
The dynamo impedance Z is a complex number made by adding the reactance X_{L} of inductance L_{D} to the resistance R_{D} ~ Reactance is the opposition to a rate of change of current through an inductor L or capacitor C ~ No other components exhibit reactance but will have an impedance due to elements of L or C like the dynamo or a wire wound resistor
In the case of a dynamo the the intention is to have only a coil of wire that generates the a.c. voltage but the wire also has series resistance R_{D }and winding it produces capacitance across the coil ~ Knowing the impedance is useful when analysing the dynamo looking into point b relative to chassis and more so at high frequency with X_{C} included Standard wire wound resistors also 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 the resistor do not dissipate any power and neither does the reactance of L_{D} in the dynamo 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 value of X_{L} increases and X_{C} decreases as frequency rises ~ The actual values at any frequency ƒ are given by The white trace below represents the current flowing in a 1Ω resistor in series with an inductor that has reactance The white trace can also represent 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 ~ click the link to see I_{R} * V_{R} shown red 

The current through the inductor is the same phase as the resistor current because they are in series but the voltage is 90˚ out of phase ~ the peaks of voltage across the inductor occur at the zero current crossing points where the rate of change of current is maximum ~ When the inductor voltage is peak its current is zero and vice versa Where the resistor current or voltage are zero 3 times per cycle there is no power generated and in the inductor this occurs 5 times per cycle but what happens in between these 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 effect it generates its own rotating magnetic field and because of this a dynamo with a fixed 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) as 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 at the point when the current is at a peak ~ the rate of fall of current to zero will be much greater than at the normal 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 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 it also has imaginary reactive power when I_{C} * V_{C} is integrated over a whole number of cycles Ideal inductors should only have inductance and no resistance or capacitance ~ Ideal capacitors should only have capacitance no inductance and infinite resistance ~ At any frequency including zero Hz any ideal reactance does not dissipate any power ~ This condition for zero power despite current flowing only occurs when the voltage and current through a component are 90˚ apart and that component can only be an ideal inductor or capacitor 

The series R and L circuit normalised to 1Ω described above or the dynamo or a magnetic pickup can be expressed on a graph where the relationship between R L and Z is easier to envisage ~ This graph is known as an impedance diagram
R and L are in series so the x axis can show 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 L and R by 90˚ as in the waveforms above We can now calculate the voltage supply 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 

As stated the impedance Z is a complex number ~ It has to be expressed using 2 terms and for the solution on the impedance diagram above these are 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˚ ~ We can determine 

ω
ss √R^{2}+X_{L}^{2} ff ss /45˚ ff Θ 



A pole at 3.18µs (50.05kHz) "fits in" with the other RIAA time constants but why not choose 45kHz or 55kHz ? ~ For "normal" audio recording there is very little energy above 10kHz and the recording chain of microphones mixing consoles and tape machines ensures that if there were any energy above 20kHz it would be 10s of dB lower before it reached the cutting head and would most likely be distortion products
Even if some record cutting lathes have a pole above 20kHz ~ which most do ~ attempting to correct for this at replay would be a waste of time — The signal to the cutting head falls naturally above 20kHz due to drive circuitry limitation and there is often a "formal pole" beyond 40kHz which is 2nd order and corrects for phase up to 20kHz 

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Passive RIAA EQ or Active feedback EQ ?  

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Separate time constants or an all in one EQ Block ?  
The circuit above was copied directly from the National Semiconductor (now Texas Instruments) data sheet for their "HiFi Audio operational amplifier" the low noise and very 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 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 using 0.1% ! ~ The capacitor type should be questioned and the tolerance 5% 'puts paid' to any attempt at precision 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 from 27.009kΩ the capacitor 47nF33nF should be 80.973nF not 80nF ~ The other RIAA capacitor 27nF4.7nF500pF should be 27.769nF so rather than 5% polypropylene why not use 27nF750pF 1% polystyrene which are readily available and I would say are better capacitors for this application 





The solution shown above using standard E12 values (E24 1% in practice) gives a more accurate RIAA equalisation than the Texas Instruments "design" with its modelled peak–peak deviation of 0.16dB between 20Hz and 20kHz using perfect components ~ The "age old" standard values of 47k 6k8 16n and 47n have a peak–peak deviation from the perfect RIAA curve of only 0.05dB The circuit has a higher impedance passive RIAA EQ block than the TI circuit but this does not affect the noise performance which is dominated by the source S/N and opamp 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 slightly better S/N ~ And also changing R6 to 1k would give about 0.7V out for 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 opamps 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 step 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 opamps are now only 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 right
The 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 (RIAA1 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 unbypassed cathode resistor R11 raises r_{a} to r_{a'} ≈ 126kΩ so the resistance affecting the EQ is 126kΩ75k 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 

In practice a valve stage configured as shown will require a pre stage for best S/N and for sufficient output level and will need a high input impedance following stage to prevent loading of the EQ block ~ C2+R2 and C1 would best be connected to ground and depending on the HT supply used the impedance of the EQ block could be made higher for more gain provided the S/N is not compromised by the Johnson noise of R1
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 unbypassed 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 (there are not 4 or 5) RIAA TCs 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 opamps 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 Lownoise audio frequency amplifiers ref.5 ~ Editor S.W. Amos ~ BBC ~ Radio TV and Audio Reference Book published by NewnesButterworth 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) 
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