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Matching

A more theoretical approach this month, with an explanation of cable impedance matching.


This month Ben Duncan puts down his soldering iron to discuss the concepts of capacitance and impedance and how they relate to your choice of studio cable.

Money spent on squeezing extra top-end response onto tapes is easily thrown away if we don't put a little thought into the choice of cables, and their lengths, used to connect equipment together. This is especially true if your set-up has an ever-burgeoning tangle of leads, for losses are prone to multiply. Of course, to an extent, EQ can combat losses accumulated in the interconnections, but why not enjoy the benefits of an accurate, noiseless, top-end boost, namely, by not losing out in the first place?

At this juncture, one might argue that Portastudios "don't go up to 20kHz anyway, so what's the point?" This is a misapprehension: top-end doesn't suddenly stop at 16kHz, and as implied by the term 'roll-off', the high frequencies are essentially still there. And with some careful treatment en route, you can avoid losing them unnecessarily.

Cable Capacitance/Source Impedance

All cables exhibit shunt capacitance (across the cores). Working in conjunction with the signal source (the desk's output impedance, say), the nett result is a low pass - or top cut - filter (Figure 1). The frequency at which significant losses arise, in excess of 1dB say, depends primarily on 3 things:

1) The source impedance. For the line level outputs on top end gear, this can be very low, typically 100 ohms or below. With a lot of budget equipment though, source impedances of 1k to 10k are common. At these impedance levels, even fairly small shunt capacitances, in the form of short cables, can cause significant losses in the treble regions.

Figure 1. Cable capacitance (Cc) acts as a low pass filter in conjunction with the output source impedance (Rs).


2) The total shunt capacitance seen by the signal. This is down to the cable's length and it's intrinsic capacitance. Normally, the capacitance of the cable alone is dominant, but with short lengths, and/or low capacitance cables, the residual capacitance formed by the cable and other components inside the equipment next in line can become relevant.

3) The number of interconnections, hence low-pass filters, in the recording chain. Not only is the effect simply cumulative; it's often interactive as well. So the more links there are in the main signal path, the more important it is to keep individual losses as low as you can.

Cable capacitance is usually specified in catalogues in pF/m (Picofarads per metre length); to find out the total capacitance, simply multiply this value by the length. For example, Rockflex cable is stated as 67pF/metre, so a 5 metre length will appear to the signal as 335pF. Most cables exhibit considerably higher capacitances; a particularly gruesome and archaic microphone cable from a well known European manufacturer (no names mentioned) exhibits 600pF/metre, so a 15m length around the control room will take us up to 9000pF (9nF) which is no mean capacitance to drive any signal into...

The Table in Figure 2 gives pF/metre values for some common cables. Failing this, the information can usually be gleaned from pro-audio dealer's catalogues.

Figure 2. What capacitance? Ten common cables examined.
Cable Type and Description Capacitance in pF/metre
Screen to one conductor Between conductor*
1) Phonoflex, single, conductive plastic screen (CPS) 55 -
2) Rockflex single, CPS 67 -
3) Musiflex twin, CPS 128 70
4) West Penn twin, foil screened 100 72
5) RG58CU 50 ohm, RF coax, braid screened 101 -
6) Belden 8641 twin, foil screened 140 72
7) RS standard, twin, braid-screened 288 171
8) RS medium, single, lap-screened 322 -
9) Curly cable twin, lap-screened 340 190
10) RS standard, single, braid-screened 360 -

* Refers solely to twin cables, and balanced interconnections.


Measuring Source Impedance



The other parameter you'll need to know in order to assess top-end losses is source (or output) impedance. Often, the figure given in manuals under 'output impedance' refers (confusingly) to the load impedance you can drive into, which is a different thing altogether. As a rule of thumb, the source impedance will be around a fifth (budget gear) to a twentieth (pro gear) of this value. But without knowing whether you're dividing the allowable load impedance or the source impedance itself(!) by 5, one is left in the dark. If you're bitten by a desire to establish it accurately, Figure 3 displays a simple measurement set-up.

Figure 3. How to measure output (source) impedance (Rs).


When an output is loaded with a resistor equal to its (internal) source impedance, the output will drop by 6dB. Armed with a box of resistors and some metering, results come quickly, though for reasonable accuracy, you must keep the test level low, say 20dB below the MOL (Maximum Operating Level); otherwise, you'll end up testing the ability of the gear to drive low impedances at high levels, which is a different ball game.

Returning to the resistors, we only need to know the rough value of Rs; you don't need to come up with 'Rs = 1.0235k' - it's quite adequate to conclude that Rs is, say, 'above 680 ohms and below 2k2, so let's call it 1k'. So your box of resistors needn't be that comprehensive after all.

If you don't have an audio millivoltmeter, it's okay to use an LED meter in lieu. Given that the 6dB resolution required will happen best around the 0dB level mark, you'll most likely have to patch a channel (or some other convenient source of gain) between RT and the metering to bring the level up to the 0dBu region.

Examining Breakpoints



Armed with some data, we can now gain an insight into the severity of the capacitance effect, by looking at the table in Figure 4. Here, source impedances are tabulated against shunt (cable) capacitances, and the frequencies given are those at which the signal is 3dB down (in level), for the stated conditions. In audio and electronics parlance, this magic -3dB frequency is called a breakpoint.

3dB is, needless to say, a hefty loss in the audio band, especially if it arises much below 18kHz, say, and more so if we take into account the cumulative effect of all the cables in the chain. A handy rule of thumb here is that if the breakpoint occurs around (or above) 100kHz, the loss at audible frequencies (20kHz and below) will be negligible. This is the meaning of the two 'staircase' dividing lines on the table, in Figure 4.

Figure 4. Breakpoints for connecting cables.
Source impedance of equipment output (Rs) (ohms)
Professional equipment
Budget & Semi-pro gear
DIN outputs and valve equipment
Total cable capacitance
(Cc) 50 100 250 500 1k 2k5 5k 10k 25k 100k
100pF 30M 15M 6M 3M 1-5M 600k 300k 150k 60k 30kHz
250pF 12M 6M 2-4M 1-2M 600k 240k 120k 60k 24k 12kHz
500pF 6M 3M 1-2M 600k 300k 120k 60k 30k 12k 6kHz
1000pF/1nF 3M 1-5M 600k 300k 150k 75k 35k 18k 9k 4-5kHz
2-5nF 1-2M 600k 240k 120k 60k 24k 12k 6k 3k 1-5kHz
5nF 600k 300k 120k 60k 30k 12k 6k 3k 1-5k 750Hz
10nF 300k 150k 60k 30k 15k 6k 3k 1-5k 750k 350Hz
(10,000pF)

Signal is 3dB down at the frequency indicated; or approx. 0-5dB down at ⅓ of this frequency

Notes:
* Values are rounded off.
* Cable capacitance: 3nF represents 10m of 300pF/metre cable, or 5 metres of 600pF/metre cable.
* Example: Output source impedance = 1k, cable capacitance = 2-5nF, signal is -3dB down at 60kHz. This represents a 0-5dB loss at the highest audible frequency, 20kHz.
* M = MHz, k = kHz


To the left, losses are academic, lying well above audio frequencies. In the tinted central section, losses are small, and often negligible, but can become significant if several interconnections have breakpoints within this zone. In the right hand section of the table, meanwhile there's going to be a definite and audible loss of top-end with one interconnection alone.

A precise evaluation of the loss effect is complicated by interaction with low pass filters, deliberately introduced by the manufacturer at the front end of equipment, to curtail RF (radio) interference and related nasties (Figure 1). If the connecting cable's breakpoint is higher than the input filter's, then the filter will dominate and there'll be no added losses. But if the two share similar breakpoints, you can expect considerable top-end attenuation.

Summary



As a general rule, it makes sense to use the lowest capacitance cable you can conveniently handle for each application. Cable choice is most significant when we're dealing with lengthy runs around the control room, or interfacing budget equipment. With short patch leads, cable choice may not matter at all on the basis of high frequency losses, but using low capacitance cable will do no harm. This is underlined by more subtle factors we haven't yet looked into, such as cable capacitance versus the drive capability of the output circuit. In extreme cases, the cable's capacitative loading can aggravate distortion, or cause oscillation, for instance.

Next time, we'll examine the role of buffers in tackling interconnection hassles, and also look at matching from the viewpoint of input and output impedances.



Previous Article in this issue

4 Channel Attenuator Project

Next article in this issue

Equipment Guide


Home & Studio Recording - Copyright: Music Maker Publications (UK), Future Publishing.

 

Home & Studio Recording - Jun 1984

Donated & scanned by: Mike Gorman

Feature by Ben Duncan

Previous article in this issue:

> 4 Channel Attenuator Project...

Next article in this issue:

> Equipment Guide


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