Calculate Tonearm - Cartridge Capability

Graham Engineering Phantom Elite 10" Tonearm

Every vinyl enthusiast is faced with this choice. When your record player element has become defective or if you want to replace your old element with a new and modern element after years of listening pleasure. Then it is extremely difficult to choose the right element for your record player, or rather, the tonearm. Because tonearm and pickup must enter into a close relationship and whether this relationship will be a success depends on your choice ……

Any cartridge/tonearm combination will exhibit resonance at a specific frequency (or frequencies). This resonance is due to the interaction of the cartridge (acting as a spring), and the weight of the arm (acting as a mass). The "springiness" of the phono cartridge is described as compliance, the weight of the arm is specified in mass. As an example, a heavy weight on a light spring would obviously over-flex the spring, conversely, a light weight on a strong spring would not allow sufficient flexion.

At resonance, the arm/cartridge combination produces a dramatic rise in output. An increase of 3 to 6dB or more is common. This tremendous boost can cause severe problems if it occurs in the region of recorded music (above 2OHz), or in the area where record warps and rumble are problematic (below 5Hz). A cartridge/arm whose resonance occurs in the region above 20Hz can be influenced by music on the record. At this frequency a significant jump in output (resulting in a "bloated" or "tubby" sound) will be experienced. In extreme cases, the stylus may actually jump out of the groove. Similarly, a cartridge/arm combination that exhibits a resonance below the desired range will exaggerate the effects of record warps, or rumble produced by the turntable.

The goal in matching a specific cartridge and arm is to achieve a resonance in the 7 to 12 Hz range. Some feel that limiting this range even further, to 9 to 11Hz, is beneficial in reducing the effects of resonance.

The following formula for calculating the resonant frequency of an arm/cartridge:

Resonant Frequency = 1000 / (2 x π x √ (M x C)).

π = 3.14159265359
M = Total tonearm system mass which is a sum of Mass of cartridge, Mass of headshell and screws and Effective mass of tone arm (all values in gram).
C = Cartridge compliance lateral in µm/mN

As an example, if we had an arm/cartridge with a combined mass of 18.1 gram, and a cartridge with a compliance of 15, the resonant frequency would be 9.69 Hz.

This simple equation doesn't take into account all factors, including tonearm damping and, internal cartridge damping, but it will give you general idea of compatibility.

You can find al lot of Tonearm Data at Tonearm Database of Vinylengine

and Cartridge Data at the Cartridge Database of Vinylengine

  • Low compliance < 10 x 10-6 cm/Dyne
  • Medium / moderate compliance 10 - 20 x 10-6 cm/Dyne
  • High compliance > 20 - < 35 x 10-6 cm/Dyne
  • Very high compliance > 35 x 10-6 cm/Dyne
Note: Dynamic compliance @ 10 Hz

Calculate Tonearm Resonant Frequency

The calculated resonance frequency only applies to cartridges where compliance is measured at 10 Hz.

• Resonance frequency within 7-12Hz is optimal for the system.
• Resonance frequency slightly outside optimal interval 6,5-7Hz and 12-14Hz can be considered as a possible that probably can be used without problems.
• Resonance frequency outside the interval 6,5-7Hz and 12-14Hz is questionable, and the system might not work properly.

Eff. Tonearm Mass :  g  
Cartridge Mass :  g  
Fastener Mass :  g  
* Compliance :  x 10-6 cm/Dyne  
*Dynamic compliance @ 10Hz

Calculate Effective Tonearm Mass

The calculated tonearm mass only applies to cartridges where the compliance is measured at 10 Hz.

Resonance :  Hz  
Cartridge Mass :  g  
Fastener Mass :  g  
* Compliance :  x 10-6 cm/Dyne  
*Dynamic compliance @ 10Hz

Here you will find all info about Turntables, Cartridges, Tonearms and more...

<<< Back