The following are patents on Induction Balance type detectors including TR and VLF.

Download Patent # Title Description
PDF 1710K US3405354 Apparatus for Limiting Phase-Angle Response Range, Particularly in Eddy Current Testing Apparatus Uses syncronous demodulation to determine target phase, see 3848182.
PDF 874K US3471772 Instrument for Measuring the Range and Approximate Size of Buried or Hidden Metal Objects Synchronous detectors, lots of fundamental theory & equations.
PDF 436K US3471773 Metal Detecting Device with Inductively Coupled Coaxial Transmitter and Receiver Coils Basic TR with 4B-style coil (NOT coaxial!).
PDF 1282K US3826973 Electronic Gradiometer Actually, a metal detector.
PDF 1330K US3835371 Apparatus for Detecting the Presence of Electrically Conductive Material Within a Given Sensing Area Focuses on submersible probe & cabling method
PDF 728K US3848182 Apparatus for Limiting Phase-Angle Response Range, Particularly in Eddy Current Testing Apparatus See 3405354.
PDF 484K US3872380 Metal Detector Distinguishing Between Different Metals by Using a Bias Circuit Actuated by the Phase Shifts Caused by the Metals Gardiner, basic phase response IB.
PDF 664K US4016486 Land Mine Detector with Pulse Slope, Width and Amplitude Determination Channels
PDF 1347K US4024468 Induction Balance Metal Detector with Inverse Discrimination White's TR Discriminator (1975), includes good description with phase diagrams and circuitry with component values.
PDF 2003K US4030026 Sampling Metal Detector White's, the basis of most of their early-80's analog detectors.
PDF 683K US4053828 Metal Detector with First and Second Nested Rectangular Coils Not too practical for a handheld.
PDF 319K US4096432 Metal Detector for Discriminatory Detection of Buried Metal Objects Basic phase response IB.
PDF 840K US4099116 Metal Detector With Phase Related Selective Discrimination Circuit Nautilus, feedback method for ground balance and discrimination.
PDF 1271K US4110679 Ferrous/Non-ferrous Metal Detector Using Sampling White's
PDF 779K US4128803 Metal Detector System With Ground Effect Rejection PNI (the old Bounty Hunter), probably the Red Baron series (RB3/5/7).
PDF 1021K US4249128 Wide Pulse Gated Metal Detector With Improved Noise Rejection White's
PDF 1277K US4263551 Method and Apparatus for Identifying Conductive Objects by Monitoring the True Resistive Component of Impedance Change in a coil System Caused by the Object Title says it all, looks at target response vs. frequency
PDF 882K US4300097 Induction Balance Metal Detector with Ferrous and Non-ferrous Metal Identification Techna, now First Texas Mfg. (Bounty Hunter)
PDF 1576K US4303879 Metal Detector Circuit with Mode Selection and Automatic Tuning 1979 Garrett patent (ADS?)
PDF 1352K US4325027 Metal Detector for Locating Objects with Full Sensitivity in the Presence of Distributed Mineral Material Compass
PDF 1176K US4334191 Metal Detector Circuit Having Momentary Disabled Output Garrett
PDF 1267K US4334192 Metal Detector Circuit Having Automatic Tuning With Multiple Rates Garrett, probably their Master Hunter VLF.
PDF 1218K US4344034 Selective Ground Neutralizing Metal Detector Gardiner patent for phase discriminator.
PDF 1008K US4348639 Transmitter-Receiver Loop Buried Metal Object Locator with Switch Controlled Reference Vooltage Discovery Electronics' two-box detector.
PDF 876K US4423377 Compact Metal Detector of the Balanced Induction Type Garrett, handheld with integrated double-D coil. See also 4488115.
PDF 3160K US4470015 Metal Detector System With Undesirable Target and Mineralized Ground Discrimination Teknetics, lots of diagrams and waveforms.
PDF 941K US4486712 Frequency Dependent Pulsed Gain Modulated Metallic Object Detector
PDF 1210K US4486713 Metal Detector Apparatus Utilizing Controlled Phase Response to Reject Ground Effects and to Discriminate Between Different Types of Metals Tesoro, lots of signal & phase diagrams
PDF 758K US4488115 Low Battery Voltage Indicator Circuit for a Metal Detector Garrett, see also 4423377
PDF 6059K US4507612 Metal Detector Systems for Identifying Targets in Mineralized Ground Teknetics, tons of info.
PDF 734K US4514692 Metal Detector and Discriminator Using Differentiation for Background Signal Suppression Fisher, basis for early X models.
PDF 337K US4563645 Inductively Balanced Oscillatory Coil Current for Metal Detection
PDF 1126K US4628265 Metal Detector and Classifier with Automatic Compensation for Soil Magnetic Minerals and Sensor Misalignment Fisher
PDF 654K US4659989 Inductively Balanced Metal Detector Circuit with Orthogonal Balancing Signals and Including Phase and Polarity Detection
PDF 1728K US4677384 Target-Identifying Metal Detector Teknetics
PDF 1235K US4700139 Metal Detector Circuit Having Selectable Exclusion Range For Unwanted Objects Garrett patent with a pretty good explanation of I&Q signal processing.
PDF 2644K US4709213 Metal Detector Having Digital Signal Processing Garrett
PDF 1073K US4783630 Metal Detector With Circuits for Automatically Screening Out the Effects of Offset and Mineralized Ground White's
PDF 2838K US4868910 Metal Detector with Microprocessor Control and Analysis White's, ton's of info on their target ID.
PDF 352K US4881036 Phase Shift Compensation for Metal Detection Apparatus
PDF 1325K US4894618 Metal Detector Using Cross-Correlation Between Components of Received Signals Minelab, good explanatory text.
PDF 1055K US4912414 Induction-Type Metal Detector with Increased Scanning Area Capability Describes a large array for use with a submersible, includes IB and PI methods.
PDF 1317K US5148151 Metal Detector Having Target Characterization and Search Classification Garrett patent on VDI, explanantion on phase response and VDI flowchart.
PDF 1669K US5506506 Metal Detector for Detecting and Discriminating Between Ferrous and Non-ferrous Targets in Ground Minelab, combines synchronous demodulators with PI, calls it multi-frequency. Compare with US5576624
PDF 1055K US5523690 Metal Detector with Bivariate Display White's patent detailing VDI, includes 6805 assembly code. (see also 5596277)
PDF 959K US5596277 Method and Apparatus for Displaying Signal Information from a Detector White's patent detailing VDI, includes 6805 assembly code. (see also 5523690)
PDF 980K US5691640 Forced Balance Metal Detector
PDF 690K US5721489 Metal Detector Method for Identifying Target Size Garrett's target ID patent, lots of signal analysis and flow charts. See also 5786696.
PDF 502K US5729143 Metal Detector With Nulling of Imbalance Bucking signal calibrated for amplitude & phase
PDF 656K US5786696 Metal Detector for Identifying Target Electrical Characteristics, Depth and Size Garrett's target ID patent, lots of signal analysis and flow charts. See also 5721489.
PDF 559K US5969528 Dual Field Metal Detector Garrett's two-box add-on.
PDF 922K US6172504 Metal Detector Target Identification Using Flash Phase Analysis White's, applies phase info to what's essentially a flash ADC ; see 6421621.
PDF 716K US6421621 Metal Detector Target Identification Using Flash Phase Analysis White's, applies phase info to what's essentially a flash ADC ; see 6172504.
PDF 723K US6583625 Metal Detector and Method in Which Mineralization Effects Are Eliminated
PDF 105K US7078906 Simultaneous Time-Domain and Frequency-Domain Metal Detector Combo PI & phase sampling
PDF 106K US7088103 Metal Detector Having a Plurality of Phase Discrimination Regions with Corresponding Selectable Exception Spaces Therein White's
PDF 193K US7126323 Systems and Methods for Synchronous Detection of Signals
PDF 227K US7432715 Method and Apparatus for Metal Detection Employing Digital Signal Processing Minelab
PDF 1587K US9557390 Noise Reduction Circuitry for a Metal Detector Minelab, Go-Find TX?
PDF 738K EP0580396 Metal Detector with Display White's VDI