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~ Bicycle Dynamos and RIAA Replay Amplifiers ~

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 upside-down the lights did not appear to get much brighter but upside-down 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

Bicycle dynamo picture
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

Bicycle dynamo schematic Pictured is a schematic typical of a bicycle dynamo with 2 lamps connected ~ LD represents the inductance of the fixed iron cored coil which is also the a.c. voltage source ~ RD is the small d.c. resistance of the coil winding ~ The ratio of LD to RD 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 XL of inductance LD to the resistance RD ~ 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 RD 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 XC included

Standard wire wound resistors also have some series inductive reactance XL and to a lesser extent some parallel capacitive reactance XC but they should be 'mainly resistive' ~ The reactive parts of the resistor do not dissipate any power and neither does the reactance of LD in the dynamo but they do influence the flow of a.c. as frequency changes

Reactances XL and XC are measured in ohms Ω and like resistors oppose the flow of current but only alternating current ~ The value of XL increases and XC decreases as frequency rises ~ The actual values at any frequency ƒ are given by XL = 2πƒL Ω and XC = 1/2πƒC Ω ~ but current flowing through a reactance will not produce power in it

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

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 IR * VR 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 ?

Graph of power in 1Ω resistor with 1V across it

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 VL = –L(∂I/∂t) as the current through the inductor falls the voltage across it rises and multiplying I* VL 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 VL = –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 IC * VC 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 VIN across the series R L circuit and the impedance of the circuit ~ In order to have VL leading VR by 90˚ VIN must lead VR by 45˚ and lag VL by 45˚ in this case where R and XL are the same ~ The magnitude of the impedance |Z| is given by √R2+XL2 and = |Z|

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 VIN = 1.414Vpk at the frequency where XL =1Ω the input current will be 1Apk and the circuit waveform relationships will look like those shown above with VIN leading VR (and IR ) by 45˚ and lagging VL by 45˚

On an impedance diagram XL is strictly XL/90˚ and XC would be XC/270˚ or XC/–90˚ ~ We can determine |Z| at other frequencies and for other values of R and L ~ It is easier than drawing waveforms but XL needs to be calculated for each frequency so it is still limited

ω

ss √R2+XL2 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

•      •      •      •      •
Passive RIAA EQ or Active feedback EQ ?
•      •      •      •      •
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 "Hi-Fi 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 47nF||33nF should be 80.973nF not 80nF ~ 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

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 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 Ao 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 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 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 op-amps 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 (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 ra of about 31kΩ for Ia = 1mA

The unbypassed cathode resistor R11 raises ra to ra' ≈ 126kΩ so the resistance affecting the EQ is 126kΩ||75k 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 gm valve with high Ia for best S/N

High gm valves tend to have a low ra 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 ra' but at the expense of gain ~ The 1.8kΩ cathode resistor of the ECC81 stage above makes ra' 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 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)


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