Introduction: background information
Transformers are made from coils of insulated wire wound on a laminated soft iron core. The iron is specially prepared and is known as m-metal. A transformer transfers energy between two parts of an AC circuit. Alternating input current in the primary coil sets up an alternating magnetic field through the secondary coil which induces an output current. The input power is V1I1 and the output power is V2I2.
The transformer, shown actual size, is made from hand wound 22 gauge copper wire on ferrite cores salvaged from an old TV set. Ferrite is a ferromagnetic oxide which has very low electrical conductivity. Ferrite is used as the core of the very high frequency line-output transformers in CRT television sets but is not normally substituted for the soft iron core of a low frequency power transformer.
Research question
What is the efficiency of this hand-wound ferrite cored power transformer, and is the efficiency dependent on the input power.
Hypotheses
1 The efficiency will be close to 95%.
The improvised transformer is closely wound and the core is large and strongly ferromagnetic. Most of the field of the primary will thread the secondary and the coils become only slightly warm during operation. If, as expected, the magnetic field in the core is proportional to the current and as strong as that in the equivalent soft iron core then the efficiency close to that of a conventional iron cored transformer.
2 The efficiency will drop slightly at larger input currents.
If the magnetic field in the core is proportional to the input current at all times, all the field threads the secondary, and there is no resistive heating the efficiency will be independent of input current. Since there is some resistive heating proportional to current squared the efficiency is expected to be slightly reduced at higher currents.
Procedure
The circuit shown (upper diagram) was connected with AC power supply, a light bulb as a load resistor. Two meters were used to measure input current and voltage at four power supply settings.
The meters were then removed and placed in the output circuit (lower diagram). Output current and voltage were measured for the same power supply settings.
The small light bulb used as a load. The connections are made with crocodile clips. The wires were cleaned with sand paper to reduce any errors due to poor contacts.
The AC power supply with four fixed output voltages
The Volt meter (left) and current meter (right).
AC meters of appropriate ranges were needed. The Department has sets of moving coil AC meters in the 0-15 Volt range and current meters in the 1-5 Amp range. The current meters will not read accurately from 0-1 Amps. A digital meter with a 0-200 milliamp AC range was selected. Only one digital meter was available, hence the need to measure input and output currents separately.
Data
Input and output voltages and currents are listed in Table 1.
Analysis
The power input and output, V1I1 and V2I2, respectively were calculated with errors.
The calculations were performed in Graphical Analysis using double entries in Table 2.
The values are plotted [with errors] in Graph 1. The red line of slope 1 corresponds to an efficiency of 100%. A curve has been fitted to the data points by hand. Clearly the measured efficiency is around 50% and not independent of input power.
Calculating the efficiency as ...
Table 3
The efficiency is plotted against input power in (Graph 2) The errors are again calculated by entering extreme values in the table (see caption Graph 1). The line on Graph 2 has been fitted to the data points by hand. The transformer is most efficient for input power in the 400 Milliwatt region.
Evaluation
If the transformer were 100 % efficient the data points would lie on the red straight line with a slope of 1.00 in Graph 1. Clearly the efficiency is about 50% and is not constant as a function of input power, since the data points lie very much below the line, and are not themselves on a straight line.
These observations are confirmed in Graph 2. The efficiency at very low power input is between 30 and 40 %. it rises slightly to better than 50% for input power in the 400 Milliwatt range but is always below 60%. For input power of a Watt and more the efficiency again declines to no better than 40%.
Errors are shown on the graph calculated from estimated uncertainties in currents for each point. The selected meters were appropriate and the bulb was a suitable load. Variations in the resistance of the filament would not affect the relative power values. Since the power supply had fixed settings it was not necessary to measure input and output power at the same times.
The efficiency was clearly less than the expected 80%+ (Hypothesis 1) and was not independent of input power (Hypothesis 2).
The explanation probably lies with the magnetic properties of the ferrite compared to the preferred laminated soft iron.
At low input currents the alternating magnetic field in the ferrite appears to be less than expected since any resistive heating effect is proportional to current squared and will be small for small currents.
For large input currents the low efficiency probably results from both lower than expected magnetic fields and resistive heating. Since the ferrite is a very poor conductor of electricity any losses due to eddy current heating will be very small. [It is for this reason that ferrite is used as a core for high frequency TV line output transformers.]
Suggestions for future work
It would be interesting to compare the relatively low efficiency of this transformer with a similar hand-wound transformer, wound on laminated soft iron rather than ferrite.
It would also be interesting to measure the magnetic field strength in the ferrite B as a function of the magnetic force H. A Hall effect probe is available for the measurement of B.
Acknowledgements
The transformer figures in the introduction were taken from the CD Physics at ISB. Thanks are due to Jonathan Eales for reading the original manuscript, and for helpful suggestions.