~ Bicycle Dynamos and RIAA Replay Amplifiers ~

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

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

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 X_L = 2πƒL Ω and X_C = 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 X_L = 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 I_R * V_R shown red

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

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 √R²+X_L² 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 |Z|/Θ at other frequencies and for other values of R and L ~ It is easier than drawing waveforms but X_L needs to be calculated for each frequency so it is still limited

ss √R²+X_L² ff

ss /45˚ ff

Θ

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

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 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 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 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

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

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 unbypassed cathode resistor R11 raises r_a to r_a' ≈ 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

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 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)