Step Up Transformers
The step up transformer is a simple and effective way to amplify the cartridge’s signal adding very low noise and distortion; a close look to its details explains the mechanism behind a good and a bad match and the effect of the load on the secondary winding. Cartridges' and transformers' electrical characteristics play a key role and can generate an ultrasonic resonance or a response damped at high frequencies, and an accurate tuning of the resistor at the output of the transformer can smooth this irregularity. Eventually, fine-tuning by ear will allow the listener to select the best match according to her/his personal preferences.
The Electrical Model of the Cartridge and Step Up
A moving coil cartridge can be modeled as a voltage generator with an internal resistance Rcartridge, ranging from a few ohms to several tens, and an inductance Lcartridge, from few μH to 100μH and more. Typically, lower output cartridges have smaller coils and hence lower resistance and inductance. The transformer is more complex and more parameters must be included in the model:
Lp – inductance of the primary winding, 0.1H to 2H typically Ls – inductance of the secondary winding, the ratio of Less/Lp equals the square of transformer ratio Rpw – resistance of primary winding, a few ohms Rsw – resistance of secondary winding, several hundreds of ohms Lss – stray inductance of the secondary winding, in the range of 10mH Css – stray capacitance of the secondary winding, a few hundreds pF Cpss – primary to secondary stray capacitance, a few hundreds pF Np – number of turns of primary winding Ns – number of turns of secondary winding
For the sake of simplicity, parasitic capacitance and leakage inductance of primary winding are omitted. Figure 1 shows the electrical model of the cartdrige and a 1:10 step up transformer with typical values for the C, L and R parameters. The loading resistor Rload is assumed to be the standard 47k found in most preamplifiers.
The Influence of Cartridge Parameters
As anticipated, the stray inductance and capacitance of the cartridge will generate a peak in the frequency response. In our model a +3dB resonance appears at 55kHz, well above the 20kHz limit, but its effects can start from 10kHz and generate a +0.75dB deviation at 20kHz.
Rcartridge and Lcartridge will have an influence upon the resonance: a large R cartridge will exhibit a small resonance but high frequency response will be impaired for higher values; a larger inductance will move the peak towards the 20kHz limit affecting the audio band.
Tuning the Load at the Secondary Winding
Rload will appear at the cartridge reduced by the square of the transformer ratio (Np/Ns)2 so the 47k Rload, reflected by the 1:10 step up, looks like a 470Ω at the primary. A 20k will be stepped down to 200Ω and so on. A lower load will reduce the peak but a too small load will affect high frequencies as the transformer will not work in its best condition. The optimal load depends on the specific cartridge and step up. A flat frequency response might not correspond to the preferred sound and the listener is encorauged to tune Rload according to her/his taste and sensibility.
In figure 5, you will also notice a lower Rload will diminuish the available signal due to insertion loss. This can somehow confuse the listener as the phenomenon might be interpreted as a loss in dynamics. Figures 6 and 7 show the effects of Rload during a square test: the lower R dampens the resonance and the ripple at the rising and falling edges.
The Best Step Up Transformer
A good transformer must have reasonably low stray C and L and a sufficiently high primary inductance Lp for an extended flat bandwidith.
A higher Lp is required to properly load high R cartridges (see also figure 3) and this should be the very first parameter to check when selecting a step-up. At low frequency f the transformer behaves as the parallel of the reflected Rload and of the primary reactance 2πfLp. In this example at 20Hz we have 470Ω in parallel with 62Ω for an equivalent resistance of 55Ω substantially higher than the 20Ω cartridge.
The effect of Css, Lss and Cssp is similar: higher stray capacitance and inductance will move the resonance closer to the audio band affecting the response from 10kHz onwards and making the tuning of Rload even more critical. Leakage inductance is proportional to the N2 while special winding techniques are employed to reduce parasitic capacitance: a good transformer is the result of years of experience and experimentations.
The Core of the Transformer Matters
Primary inductance is proportional to the square of turns Np, to the cross section of the core, to the magnetic path and to the permeability of the core material. The designer has to determine the best balance of core size and number of turns to assure the transformer will operate with low distortion and extended frequency range. Unfortunately, increasing the number of turns will also increase the flux density and bring the core closer to the saturation at low frequencies. On the other hand, a bigger core will have a larger cross section and a longer magnetic path but will also determine an increase of stray capacitance.
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Author: Gianluca Sperti