FIG.  1a is a simplified passive pickup circuit found in most of the electric stringed musical instruments.  The pickup circuit is called a Strings Sensing Means in this embodiment, it comprises of a non-humbucking pickup coil named Signal Coil.  Most electric stringed instruments comprise of a passive Strings Sensing Means with a single of plurality of Signal Coils.  But the basic theory is similar to the circuit shown in FIG.  1a.  In FIG.  1a, Coil 100 senses the vibrating strings and the unwanted electromagnetic radiation from the surrounding; thereby, producing a Signal Voltage and a Noise Voltage.  The Noise Voltage produces humming or buzzing sound when connected to an amplifier.  Sound characteristics produced by coil 100 is affected by the impedance loading coil 100.  FIG.  1a comprises a Sound Control circuit that control the volume and the tone of the stringed instrument.  The Sound Control circuit also serves as load across coil 100 to produce the most desirable sound characteristics.  In this embodiment, the Sound Control circuit is also called Optimal Load.  The most common form of Optimal Load is implemented with a potentiometer (pot) 104 in parallel with a tone circuit between junction 103 and 111.  The tone circuit comprises pot 106 and capacitor 107.  For Fender Stratocaster type Signal Coils, it was found that 250KΩ for pot 104, 106 and 0.022 μF for capacitor 107 produce the best sound characteristics.  At frequency above 500 Hz, the reactance of the capacitor 107 is much lower than 250KΩ.  Thereby, the Optimal Load for Fender types of Signal Coils is the parallel of the pot 104 and 106, which is 125KΩ.  For Gibson with P90 type of Signal Coils, people find 500KΩ for pot 104 and 106 produces the best sound characteristics.  Thereby the Optimal Load is 250KΩ. 
Referring back to FIG.  1a, any active electronics such as transistor and op-amp in either the signal forward or return path in the passive pickup circuit alters the sound characteristics.  The signal forward path is from coil 100 at junction 102 to 103, through potentiometer 104 to Output Jack 112.  The signal forward path also goes from junction 103 through potentiometer 106 and capacitor 107 to junction 111.  The signal return path is from the ground of Output Jack 316, through junction 111 to junction 107, back to the return of the Signal Coil 100 at junction 105.  This Embodiment uses active circuit for noise cancellation while keeping the both signal forward and return path unchanged and totally passive.  Noise cancellation of this Embodiment is by injection of a current signal directly into the Signal Coil using a Transconductance Means called Injection Amp.  The Injection Amp is designed to inject the Current Signal directly into the Signal Coil without affecting the original sound characteristics.  This eliminates the need of adding any active circuit in the signal forward and return path inside the passive Strings Sensing Means of the stringed instrument. 
Prior Arts Using Passive Noise Cancelling
Three prior designs are described here shown in FIG.  1b.  Same alpha numeric for the same components and wires are used as in FIG.  1a.  In FIG.  1b, coil 100 produces a Signal and a Noise Voltage.  A Cancellation Coil 120, is designed to detect only the unwanted electromagnetic radiation and produces a Cancellation Voltage with the same amplitude but opposite phase to the Noise Voltage.  Since both coil 100 and 120 are connected in series, the Cancellation Voltage cancels the Noise Voltage.  The problem in this design is, coil 120 acts as a filter, which changes the sound produced by Signal Coil 100.  Three examples using this concept are:    1) Fender Powerhouse Stratocaster that uses a coil 120 placed far away from the strings to sense the unwanted electromagnetic radiation only.     2) U.S. Pat.  No.  4,442,749 by Lawrence Dimarzio where coil 120 is located right under Coil 100.     3) U.S. Pat.  No.  7,259,318B by Chiliachki where coil 120 has a large area in the middle.  The larger the area, the less turns is needed, whereby, less filtering of the sound of coil 100.Prior Arts Using Active Noise Cancelling
Referring back to the description of FIG.  1a, any active electronics such as transistor and op-amp in either the signal forward or return path in the passive pickup circuit alters the sound characteristics.     1) One prior design is represented by U.S. Pat.  No.  4,581,974 filed by Leo Fender.  The simplified circuit is shown in FIG.  1a.  Coil 100 produces the Signal and Noise Voltage; and the coil 120 produces only the Cancellation Voltage.  The two outputs are summed together and Noise Voltage is cancelled by a summing amplifier 50 using resistors 51, 52 and 53.  The summing amplifier isolates coil 120 from affecting coil 100.  The Signal Voltage from coil 100 goes through op-amp 50.  Since there is active electronics in the signal path, it changes the sound of the otherwise passive circuit.  Also the instrument will stop functioning if the battery runs out.  This is a problem if this happens during the performance.     2) Another design using active electronics is U.S. Pat.  No.  5,569,872 by Dudley Gimpel.  The simplified circuit is shown in FIG.  2b.  The concept is similar to the circuit shown in FIG.  1b except using an amplifier 208 to isolate Signal Coil 100 from Cancellation Coil 120.  The idea is using the output of amplifier 208 to provide a low impedance return path for coil 100.  As shown in FIG.  2b, the signal forward path is from junction 214 through junction 103 and potentiometer 104 to output jack 112.  The forward path contains only passive components like in FIG.  1a.  This is an improvement over the one by Leo Fender.  However, the signal return path from junction 111 goes through the isolation amplifier 208 and capacitor 211 back to the bottom of coil 100.  Thereby, the signal return path contains active electronics.  Although the isolation amplifier 208 has low output impedance, still, this is not a true ground.  Furthermore, if the battery runs out, amplifier 208 turns off; and the low impedance return path for coil 100 is lost.     3) Another design using active noise canceling is U.S. Pat.  No.  6,208,135 B1 by Steve J. Shattil.  In U.S. Pat.  No.  6,208,135 B1, only FIG.  1 and FIG.  2.  are very similar to the U.S. Pat.  No.  4,581,974 described above.  The other aspects involve an Antenna to generate an electromagnetic wave in the region around the Signal Coil to cancel the unwanted electromagnetic radiation.  The signal used to drive the Antenna coil also comprises of signals of the vibrating strings, this will definitely change the sound of the instrument.  This is more suitable to product positive feedback to sustain the sound of the stringed instrument to make it sound like a violin than for noise cancellation.