Ask the Doctors: Transformers--More Than Meets the Eye
By Dave Berners
This month, rather than answering a reader's question, we will discuss transformers and their uses in audio circuits.
Transformers are commonly used for two purposes: isolation and impedance-matching. For many applications, transformers can perform these two tasks with better fidelity than any other technology. Moreover, the qualities of artifacts that are related to transformer use can be more palatable than defects associated with other devices. In fact, many audio enthusiasts view some transformer artifacts as desirable. Here we will discuss some of the interesting behaviors of transformers.
The essential construction of a transformer is two (or more) conductors physically close to each other. The idea is to place the conductors so that they will somehow be electrically coupled to one another. The coupling in a transformer works by magnetism. Any conductor carrying current will produce a magnetic field in the space around it. If the volume immediately surrounding the conductor is homogeneous, the magnetic field will be most concentrated near the conductor, and fall off in strength with greater distance. The overall strength of the magnetic field varies in proportion to the current in the conductor. At audio frequencies, and reasonable physical scales (sizes), the shape of the magnetic field in space is independent of the type of signal passed through the conductor. At any instant in time, the field will have the same shape, but its strength will be in proportion to the instantaneous amount of current flowing in the conductor. The shape of the field is determined by the geometry of the conductor and the magnetic properties of the material surrounding the conductor.
Many audio enthusiasts view some transformer artifacts as desirable.
If a second conductor is placed near the first, the changing magnetic field around the second conductor will induce a voltage across it. Thus, the second conductor becomes electrically coupled to the first. You might ask, “How do we know that the magnetic field is there?” One way we know it's there is precisely because the transformer works. The discovery of magnetic fields was made partly based on measurements of induced voltages in conductors near sources of current. Magnetic fields are invisible, but their presence can be measured by the voltages they induce in space. The particular nature of magnetic fields can be postulated based on those measurements.
We say that we have a “good” transformer if our two conductors are very strongly coupled. As mentioned above, the shape of the magnetic field produced by current in our transformer depends on the shape of the conductor and the material near it. As it turns out, a conductor in the shape of a coil tends to focus much of its magnetic field into a small volume. If that volume is filled with what we call a “magnetic” material, the magnetic field will become even more focused. Focusing the field helps increase the coupling between our conductors. In addition, a focused field will help prevent our transformer from interacting with other components nearby. So, in practice we often see transformers created by winding multiple coils of wire around some magnetic material (a magnetic core).
There is a symmetry to transformers. Just as our second conductor (the secondary winding) is electrically coupled to the first (the primary winding), the first conductor is coupled to the second. Usually, the secondary winding of the transformer is connected to the load, or the part of the circuit we wish to drive. When a voltage appears across the secondary winding, a current begins flowing through the load. That current must be supplied by the secondary winding of the transformer. For a resistive load, the current in the secondary winding will produce a magnetic field that counteracts, or bucks, the field generated by the first conductor. We say that the load is “reflected” to the primary winding. When a voltage is applied to the primary, some current goes to produce the magnetic field in the transformer. This current is called excitation current. The remainder of the current flowing in the primary is precisely the amount needed to cancel the magnetic field caused by the current flowing in the secondary winding (the load current). For a transformer that is close to ideal, the excitation current is much smaller than the load current. By changing the relative number of turns of wire on the primary and secondary windings, we can control the amount of current needed in the primary winding to produce a given amount of load current. This is true because the total magnetic field within the transformer is due to the sum of all of the current in the primary and secondary windings. For the currents in the primary and secondary windings to cancel, we must have Ip*Np = Is*Ns , where Ip and Is are the currents in the primary and secondary windings, and Np and Ns are the number of turns on the primary and secondary windings.
As mentioned above, the use of magnetic material within a transformer helps to confine the magnetic field. The material confines the field by affecting the relationship between the current through a transformer winding and the density of magnetic field lines resulting from that current. A material's magnetic permeability is defined as the amount of magnetic flux resulting from a current through one of the transformer windings. A highly permeable material will result in a high flux density for a given current through a transformer winding. Thus, for a given voltage applied to a transformer, the amount of excitation current will be reduced by using a highly permeable magnetic material (electrically, we would say that the magnetic material increases the primary inductance of the transformer).
So, we can see that use of magnetic materials in transformers can reduce interference with surrounding components, and can also decrease a transformer's excitation current, making it closer to ideal. However, there is a drawback to using magnetic materials. When using highly permeable materials, there is no longer a linear relationship between the magnetizing current in a transformer and the amount of magnetic flux. There are two major nonlinear effects due to use of magnetic materials. The first is saturation: magnetic materials can only be magnetized to a certain extent. This means that after the excitation current in a transformer reaches a certain point, the effective permeability of the magnetic material begins to be reduced. At this point, it will take increasing amounts of excitation current to continue inducing a voltage on the secondary winding of the transformer. As long as the source driving the transformer is capable of supplying the excitation current, the transformer will continue to function. But, if the source has a finite output impedance (always the case), eventually the source will not be able to supply enough current, and the voltage at the transformer will fall off.
Transformers are also terrific for isolation.
The second important nonlinear property of magnetic materials is hysteresis. Hysteresis is caused by the fact that magnetization of the transformer causes a physical change in the material within the transformer. That change is not entirely efficient, so that there is some energy loss whenever the magnetization is changed.
Saturation tends to cause distortion at higher signal levels, while hysteresis can cause distortion at low signal levels. Saturation can be considered roughly akin to clipping, while hysteresis can be loosely classified as a type of crossover distortion. Both hysteresis and saturation depend heavily on what material is used for the transformer's core.
What really sets transformer distortion apart from distortion caused by memoryless clipping or crossover distortion is the dependence on frequency of the distortion. As it turns out, the magnetization of a transformer's core is related to the integral with respect to time of the voltage placed across the transformer. In fact, a transformer's capacity is often measured in volt-seconds (the product of voltage and time). This means that at lower frequencies, a voltage signal applied to a transformer will create more distortion than a high-frequency signal at the same amplitude. Also, because of the time-dependence of the distortion mechanism, intermodulation distortion cannot be simply calculated from THD. As it turns out, intermodulation distortion for a transformer is usually lower than would be predicted based on the low-frequency distortion figure for the transformer.
Many single-ended tube circuits exhibit a similar distortion-frequency dependence, because the open-loop gain of these circuits falls to zero at DC due to decoupling capacitors. The loss of open-loop gain results in less negative feedback at low frequencies, which leads to increased distortion.
Depending on the material used in a transformer's core, at slightly saturated signal levels, distortion can be confined mostly to the third harmonic. It has been demonstrated that low-order harmonic distortion tends to be less disruptive in terms of human perception, when compared to distortion at higher harmonics. This may be a second reason why transformers can provide “pleasant” nonlinearities.
Transformers have great value apart from their distortion characteristics. Due to the relationship between current and number of turns on a winding, a transformer can be used to change the apparent impedance of a load. For an N:1 transformer, where there are N times as many turns on the primary winding as there are on the secondary, a load across the secondary will appear to have an impedance N2 times its actual value. Conversely, the source impedance, as seen by the load, will be reduced by N2. Many tube circuits use “step-down” transformers to convert a high-voltage, medium-impedance output to a medium-voltage, low-impedance output. Conversely, a transformer can also be used to “step up” a signal to a higher voltage. An example of this is the auto-transformer used to drive the EL panel in the LA-3A.
Transformers are also terrific for isolation. A transformer's behavior depends almost entirely on the differential voltage across its primary, with common-mode gain being very small. This is difficult to achieve without a transformer.
Both for functionality and euphonic signal processing, transformers continue to be popular in audio, and will remain a vital part of audio circuits for the foreseeable future.