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Controlled Impedance is mainly a function of the dielectric material type and thickness, in conjunction with the trace width and height. Impedance is basically the resistance of a conductor and the feedback/opposition of the current of that conductor. This value becomes important in higher speed PCB designs where the PCB impedance needs to match the components impedance to create the least amount of loss in the design.
When manufacturing a PCB with controlled impedance layers, a great deal of attention needs to be applied to the the geometries of the signal layer and the dielectric that shields the signal, (the ground plane). There are plenty of companies that offer very simple to use design softwares and testing equipment to ensure that the end result is exactly as designed.
To test a controlled impedance design, all that is needed is a TDR, (Time Domain Reflectometer) device which is a fairly inexpensive piece of equipment. The typical tolerance for a controlled impedance board is +/-10% of the targeted value. It is very possible to decrease this to a +/-5% but this will be a little more costly to production since a higher level of control is required.