LCR Testing

Introduction

L, C and R are alphabetical symbols for the electrical properties of Inductance, Capacitance and Resistance, respectively. The letter "L" is used in honor of physicist Heinrich Lenz, "C" and "R" are the first letters of Capacitance and Resistance. These electrical characteristics are important in both audio signal and power cable design as they can have a significant and interdependent influence on a cable’s performance.

At Pine Tree Audio we are closely focused on the performance of our cables and the electrical characteristics of them. We utilize a precision digital measurement tool and a custom test fixture we designed, built, and calibrated. We test our cables throughout the design, prototype and initial listening tests to control the performance of our cables. We also offer a detailed cable test report service for any product purchased which will show the measurements of the relevant electrical parameters of our cables.

Before thinking about how the L,C,R values will influence the performance of a cable, it is important to understand the concept of a passive component. Audio signal cables and power cables are passive components in that they do not have the ability to introduce net energy into the circuit. In other words, they cannot amplify or increase the power of a signal. Inductors Capacitors, and Resistors are three of the four basic passive linear elements (the other being transformers).

We are always trying to make the cable have as little electrical effect on the signal as possible. We want to make our cables with the lowest L,C and R values as possible and we also want our L,C,R values to be consistent from cable to cable. This may sound simple, but it is no small feat.

Resistance

The "R" or Resistance (Figure 1) of a cable refers to the degree of which the conductor will oppose the flow of electrical current. Resistance of a conductor is a function of the inherent resistivity of the material used, its length, area, and temperature. There are two types of resistive measurements which we use to compute a total series resistance measurement, these will be explained below. Resistance values posses the unit of measure called the "Ohm", after physicist Georg Ohm.

The following series ohmic measurements are used for audio signal and power cables: the DC resistance (DCR) for the pure resistance of the conductors in a cable at 0Hz and the *AC Resistance (Rac) at relevant audio frequencies is resistance as a function of **Skin Effect based on frequency. These values (DCR and Rac) are added to find the Total Series Resistance (Rs) of the conductor at each frequency. The values of DCR+Rac from each frequency measurement are then averaged to give us the Rs. Our cables measure in the milliohm range, 1 milliohm is 1 thousandth of one ohm.

*AC Resistance is closely related to a property known as Impedance (Z) which differs by frequency and takes into account reactive properties of Capacitance and Inductance which store and release energy.

**Skin Effect is a property of a conductor whereby as frequency of the applied increases, electrons begin to migrate away from the center and toward the outer edges (or skin) of the conductor. At DC, the entire conductor is effectively carrying current.

Inductance

The "L" or Inductance (Figure 2) of a cable is what is considered to be a *Reactive property. Inductance refers to the tendency for an electrical conductor to oppose a change in current (rate of electron flow) through it. This opposition (Inductance) occurs proportionally with the magnitude and rate of change (frequency) of the current as an increasingly larger magnetic field is created around the conductor as current increases. Any change in current will produce a counter electromotive force (back EMF) that will oppose the change in voltage that is creating the change in current.

A change in current which creates these magnetic fields is most important when designing our speaker and power cables, as these cables deliver significant amperes of current to the load (speaker or power transformer of an audio device such as an amplifier).

Small signal cables (RCA, XLR, etc.) are also affected by Inductance (though to a lesser degree) and we keep tight control on their Inductance values as well.

The Inductance we measure in our cables is a series value, meaning it is measured along the length of the conductors in question as one length. Inductance is measured in "Henries", named after scientist Joseph Henry. Our cables will measure in the microhenry range, which is very small, 1 microhenry is one millionth of a Henry.

*Reactance is the opposition to a change in electrical voltage or current, the operative word being “change”. In audio signal and power cables we are only interested in the transmission of AC or alternating (changing) signals, hence why Reactance becomes important.

Capacitance

The "C" or Capacitance (Figure 3) is also a Reactive property. Capacitance refers to the tendency of two or more conductors to store an electric charge in proportion to a voltage (strength of electron flow) signal through them.

There are two types of capacitance which affect audio cables: Self Capacitance is a conductor’s inherent characteristic of holding an electrical charge while Mutual Capacitance is based on multiple conductors and their geometry, spacing, and permittivity of insulating material (*dielectric). Because we are primarily dealing with at least 2 conductors (signal and ground at the very least) we are very interested in the capacitance values of our cables.

*A Dielectric is a material which acts as an electrical insulator but can be polarized by an applied electric field. This means that when a dielectric is placed in an electric field, electric charges shift slightly out of their normal positions either toward the charge (+) or away from (-).

Implications

To understand the reason that L,C and R values are significant to audio cables, we must first understand the concept of a filter, more specifically a passive filter. When two or more of the three L, C and/or R values are present in an electronic circuit, a filter is created. In audio, a filter is used to remove unwanted frequencies from a signal. An example of a passive filter would be a 2-way crossover in a loudspeaker enclosure. The passive elements act to filter out the low frequencies from getting to the tweeter (called a High Pass filter Figure 4) and the high frequencies from getting to the woofer (Low Pass Figure 5).

In most audio cables there are no physical resistors, capacitors, or inductors. These behaviors appear and can create a filter effect. This filter is an unintended consequence of the physical properties of the conductors. Also contributing to the filter effect is the fact that we have multiple conductors next to each other, and there is current flowing through the conductors.

We know that all cables will exhibit some Resistance, Capacitance and Inductance to varying degrees. The length of the cable determines the total values which are present on the cable. After the values of a cable are determined we can model the cable electrically using what is called a Lumped Element Model (see Figure 6). You will notice that a lumped element model of a speaker cable looks very much like the filters shown previously; that is because it is essentially behaving in the same manner.

Figure 6 demonstrates a speaker cable with its electrical properties shown as symbols with no value. In an actual model we would insert the values that we measure on our cable under test into all of the symbols. Using math (or computer modelling software) we can determine if the cable is flat in its response.

We will demonstrate this by filling in the actual L, C and R values from a 10 foot, 16AWG stranded copper twisted pair cable that could be used for speaker level signals. The following table shows the values as a total measurement and as a per foot measurement.

Now we arrive at the lumped element model shown in Figure 7. When we calculate the cutoff frequency of this filter (the frequency at which the filter begins to attenuate the input signal, we find that it is well over 1MHz. This means that for audio signals, this cable is not decreasing the signal from the input to the output.

One must note that while these measurements are important in their representation of the electrical properties of the cable in question, they are not a definitive indicator of sound quality. This is becuase two significant contributors to the sound quality are not accounted for in this type of measurement and modelling; the source impedance and load impedance. Our modelling assumes a source impedance of 0𝛀 and a load impedance of infinite value, thus giving us results that are telling of the cable itself, not of the cable in a system necessarily.

Considerations

With a better understanding of the electrical properties of an audio signal or power cable we can more precisely choose the correct cable for our listening system. Pay close attention to the L,C and R values of a cable you are looking to purchase. If you have questions about the L, C, R values of any of our cables, we are happy to give you the general specifications.

For those who are even more interested in the exact values of a specific cable they have purchased from us, we offer a service which will provide you with a detailed report of all the values of your cable. The fee for one cable (cables sold in pairs are also the same price) is only $25. Typically our customers choose this option at the time of purchase so they will have the test report arrive with their new cables.

All of the cables we make are eligible for a cable test report. Let us know if you have any questions about LCR testing, cable test reports, or what cable will work best in your system.