Use of a recirculating delay line with a time-to-digital converter

BACKGROUND

Field of the Invention

This disclosure relates to time to digital converters (TDC) and to improvements in the resolution of TDCs.

Description of the Related Art

A Time-to-Digital Converter (TDC) converts the “time” information between two specified events into a digital number in terms of a given time-base. For example, referring to <figref idref="DRAWINGS">FIG. 1A</figref>, the time information Δt represents the elapsed time between EVENT<b>1</b> and EVENT<b>2</b>. As shown in <figref idref="DRAWINGS">FIG. 1B</figref>, the “time information” Δt in a phase-locked loop (PLL) represents the phase difference between the rising edges of the reference (CLKREF) and feedback clocks (CLKFB). Referring to <figref idref="DRAWINGS">FIG. 1C</figref>, the input pulse width specifies the “time information” in time of flight measurements. Therefore, the two events correspond to the rising and falling edges of the input pulse.

The native resolution (T_LSB) of the TDC is determined by the smallest measure of the time-base, which represents the smallest unit of time that can be quantified in the system. <figref idref="DRAWINGS">FIG. 1A</figref> illustrates the smallest T_LSB, where LSB refers to least significant bit. There are various types of time-base(s) with various levels of stability and resolution. For example, the time basis may be the period of the system clock T_CLK. Using T_CLKas a time base provides high stability but poor resolution. Note that a higher frequency system clock can be used for better resolution at the expense of increased power dissipation. In another example, the time base T_GATE, based on the gate delay of a digital standard cell, such as an inverter or buffer, provides high resolution but poor accuracy as T_GATEcan be sensitive to process, voltage, and temperature (PVT) variations. In another example a voltage/current-referred time-base (T_REF=C_REFV_REF/I_REF) provides medium resolution and medium accuracy. Note that the idea here is to obtain a “time reference” using impedances (resistor/capacitor) and a voltage reference (bandgap).

Traditionally, in PLLs, phase delay information between a feedback clock (CLKFB) and a reference clock (CLKREF) is stored in voltage mode by using a phase detector followed by a charge-pump and a capacitor. <figref idref="DRAWINGS">FIG. 2</figref> illustrates the basic idea. The pulses output from the phase detector <b>201</b> control the current sources <b>203</b> and <b>205</b> to charge/discharge the capacitor C using a fixed current I_REF, with the polarity of the charge adjustment being determined according to whether CLKFB leads or lags CLKREF. If the phase difference between CLKREF and CLKFB is Δt, the voltage on the capacitor is given by

<maths id="MATH-US-00001" num="00001"><math overflow="scroll"><mrow><msub><mi>V</mi><mi>OUT</mi></msub><mo>=</mo><mrow><msub><mi>V</mi><mi>CM</mi></msub><mo>±</mo><mrow><mfrac><mrow><msub><mi>I</mi><mi>REF</mi></msub><mo>⁢</mo><mi>Δ</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><mi>t</mi></mrow><mi>C</mi></mfrac><mo>.</mo></mrow></mrow></mrow></math></maths><img file="USRE48735E_D0001.tif" /><br /> Thus, the capacitor stores the time information (phase delay) as charge. <figref idref="DRAWINGS">FIG. 3</figref> illustrates a timing diagram associated with the traditional voltage mode approach shown in <figref idref="DRAWINGS">FIG. 2</figref>. A reset mechanism (not shown) is provided to discharge the capacitance between phase comparisons.

Where TDCs are used to convert the time information to digital, TDCs often utilize 2-stages, a coarse TDC and a fine TDC. The coarse TDC typically works with a time base T_CLKset by a system clock. The fine TDC is often based on a delay line using N elements with a unit delay of T_GATE. The delay line may be locked to one period of the time base T_CLK. The overall resolution is determined by the fine TDC. Improvements in the resolution of the TDC is desirable to achieve a more accurate TDC.

SUMMARY OF EMBODIMENTS OF THE INVENTION

Embodiments disclosed herein improve the resolution of Time-to-Digital Converters (TDCs) by using a gain stage at the input of the TDC. The gain stage uses a “time amplifier” that provides a known fixed PVT invariant gain in the time domain. In embodiments, the time-domain gain is achieved by repetitive addition using a delay line to recirculate time information supplied by way of a pulse, which makes the overall gain PVT invariant.

In an embodiment a method for performing a time to digital conversion includes receiving an input pulse indicative of time information and recirculating a representation of the input pulse in at least one delay line. An output pulse corresponding to the input pulse is generated that is based, at least in part, on a delay line output signal of the at least one delay line. The output pulse is supplied N times to an integrating time to digital converter, where N is an integer greater than one.

In another embodiment an apparatus includes a delay line and input logic coupled to receive an input pulse and coupled to an output of the delay line, the input logic to supply a delay line input signal to the delay line. The delay line recirculates a representation of the input pulse. An integrating time to digital converter is coupled to the delay line to receive N pulse out signals, each pulse out signal corresponding to the input pulse to thereby generate a digital representation of the input pulse multiplied by a gain of N, where N is an integer greater than one.

In another embodiment an apparatus includes a delay line supplying a delay line output signal. A rising edge detector detects a rising edge of an input pulse and supplies a rising edge pulse. A falling edge detector detects a falling edge of the input pulse and generate a falling edge pulse. A first logic circuit logically combines the rising edge pulse, the falling edge pulse, and a feedback signal based on the delay line output signal. A second logic circuit receives an enable signal and an output pulse based on the delay line output signal and passes the output pulse when the enable signal is asserted.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention may be better understood, and its numerous objects, features, and advantages made apparent to those skilled in the art by referencing the accompanying drawings.

<figref idref="DRAWINGS">FIG. 1A</figref> illustrates time information between two events.

<figref idref="DRAWINGS">FIG. 1B</figref> illustrates the time information corresponding to a phase difference in a PLL.

<figref idref="DRAWINGS">FIG. 1C</figref> illustrates time information relating to a time of flight measurement.

<figref idref="DRAWINGS">FIG. 2</figref> illustrates how phase delay information between a feedback clock (CLKFB) and a reference clock (CLKREF) in a PLL is stored in voltage mode by using phase detector followed by a charge-pump and a capacitor.

<figref idref="DRAWINGS">FIG. 3</figref> illustrates a timing diagram associated with the traditional voltage mode approach shown in <figref idref="DRAWINGS">FIG. 2</figref>.

<figref idref="DRAWINGS">FIG. 4A</figref> illustrates a high level block diagram of an embodiment having a gain stage before the fine TDC to improve the effective resolution of the TDC.

<figref idref="DRAWINGS">FIG. 4B</figref> illustrates another high level block diagram with a gain stage to improve the effective resolution of the TDC.

<figref idref="DRAWINGS">FIG. 5</figref> illustrates a conceptual high level block diagram of a gain stage.

<figref idref="DRAWINGS">FIG. 6</figref> illustrates a time amplifier circuit that uses a time-to-voltage converter or charge pump followed by a voltage amplifier, followed by a voltage-to-time converter.

<figref idref="DRAWINGS">FIG. 7</figref> illustrates a conceptual block diagram of a time amplifier circuit that relies on time information being stored in the system and repeatedly supplied to an integrating fine TDC to achieve the desired gain.

<figref idref="DRAWINGS">FIG. 8</figref> illustrates how the timing information may be saved as pulses circulating in a delay line.

<figref idref="DRAWINGS">FIG. 9</figref> illustrates a timing diagram associated with recirculating pulses in a delay line.

<figref idref="DRAWINGS">FIG. 10</figref> illustrates an embodiment of a recirculating delay line circuit with a single delay line to store time information that can be used as a time amplification circuit when used in conjunction with an integrator.

<figref idref="DRAWINGS">FIG. 11</figref> illustrates an embodiment of a recirculating delay line circuit that circulates pulses in two delay lines to store time information and desensitizes the circuit to delay mismatches between rising and falling edges in the delay lines using edge detect circuits.

<figref idref="DRAWINGS">FIG. 12</figref> illustrates an embodiment of a recirculating delay line circuit that stores time information and that alleviates delay mismatch between the two delay lines shown in <figref idref="DRAWINGS">FIG. 11</figref> by using a single delay line to circulate both the rising edge and falling edge pulses.

<figref idref="DRAWINGS">FIG. 13</figref> illustrates an embodiment of a recirculating delay line circuit that stores time information with additional control to provide different delays, if desired, for rising and falling pulses.

<figref idref="DRAWINGS">FIG. 14</figref> illustrates an embodiment of an integrating fine TDC that may be used in conjunction with a recirculating delay line circuit to provide time amplification and increased effective resolution.

<figref idref="DRAWINGS">FIG. 15</figref> illustrates a high level block diagram of a TDC with a coarse TDC and a fine TDC.

The use of the same reference symbols in different drawings indicates similar or identical items.

DETAILED DESCRIPTION

The effective resolution (T_LSB,eff) of the TDC can be improved by adding a gain at the input of the fine TDC prior to its quantization. As shown in <figref idref="DRAWINGS">FIG. 4A</figref>, a gain stage <b>401</b> multiplies a pulse <b>403</b> having a pulse width T_PWand supplies the pulse with gain to an N-bit fine TDC <b>405</b>. The digital value supplied by TDC <b>405</b> is then right shifted in <b>407</b> to provide a digital average <o ostyle="single">T_PW</o> that has N+M bits. Thus, for a native resolution of <img file="USRE48735E_D0002.tif" />, and a gain of 2^M, the effective resolution <img file="USRE48735E_D0003.tif" /> can be determined as follows:

<maths id="MATH-US-00002" num="00002"><math overflow="scroll"><mrow><mrow><mover><msub><mi>T</mi><mi>PW</mi></msub><mi>_</mi></mover><mo>=</mo><mrow><mo>(</mo><mrow><mrow><msup><mn>2</mn><mi>M</mi></msup><mo>⁢</mo><msub><mi>T</mi><mi>PW</mi></msub></mrow><mo>+</mo><mover><msub><mi>T</mi><mi>LSB</mi></msub><mo>~</mo></mover></mrow><mo>)</mo></mrow></mrow><mo>&gt;&gt;</mo><mrow><mrow><mi>M</mi><mo>⇒</mo><mover><msub><mi>T</mi><mi>PW</mi></msub><mi>_</mi></mover></mrow><mo>=</mo><mrow><mrow><mrow><msub><mi>T</mi><mi>PW</mi></msub><mo>+</mo><mfrac><mover><msub><mi>T</mi><mi>LSB</mi></msub><mo>~</mo></mover><mn>2</mn></mfrac></mrow><mo>⇒</mo><mover><msub><mi>T</mi><mrow><mi>LSB</mi><mo>,</mo><mi>eff</mi></mrow></msub><mo>~</mo></mover></mrow><mo>=</mo><mrow><mfrac><mover><msub><mi>T</mi><mi>LSB</mi></msub><mo>~</mo></mover><msup><mn>2</mn><mi>M</mi></msup></mfrac><mo>.</mo></mrow></mrow></mrow></mrow></math></maths><img file="USRE48735E_D0004.tif" /><br /><figref idref="DRAWINGS">FIG. 4B</figref> illustrates an equivalent view of achieving improved resolution of the fine TDC.

Note that the idea described in <figref idref="DRAWINGS">FIGS. 4A and 4B</figref> requires a “time amplifier” such as shown in <figref idref="DRAWINGS">FIG. 5</figref>. The time amplifier of <b>501</b> accepts an input pulse <b>503</b> of width T_PWand produces an output <b>505</b> having a pulse width “G×T_PW. Referring to <figref idref="DRAWINGS">FIG. 6</figref>, a time amplifier circuit can be realized by using a time-to-voltage converter (TVC) <b>601</b> or charge pump followed by a voltage amplifier (G) <b>603</b>, followed by a voltage-to-time converter (VTC) <b>605</b>. Note that the linearity and PVT sensitivity of the TVC, voltage amplifier and VTC affect the overall performance of such a time amplifier. However, the three operations involved cause significant PVT variation in the overall gain. Embodiments described herein avoid the conversion from time to voltage and vice-versa shown in <figref idref="DRAWINGS">FIG. 6</figref> and the significant PVT variation.

In order to avoid the shortcoming of the time amplifier circuit illustrated in <figref idref="DRAWINGS">FIG. 6</figref>, <figref idref="DRAWINGS">FIG. 7</figref> illustrates a conceptual block diagram of a time amplifier circuit that relies on time/phase information in pulse <b>701</b> being stored in the system in time storage <b>703</b> and uses an integrating fine TDC <b>705</b> to achieve the required gain. Using the “stored” information, the same input is applied “N-times” to the fine TDC <b>705</b>. The fine TDC operates in the “integrating mode” where it accumulates the inputs before quantization. The integrated input is finally quantized. Since the quantization occurs after the input is accumulated “N” times, the system is equivalent to an analog gain of “N” followed by the quantizer. For the integrating fine TDC <b>705</b>, the final output is given by the “first difference” of two successive samples determined in block <b>707</b>. That allows the errors at the input to be first-order shaped (20 dB/decade) in the frequency domain. Therefore, it is possible to reduce the errors “in-band” by low pass-filtering the digital output. Note that the approach illustrated in <figref idref="DRAWINGS">FIG. 7</figref> requires a mechanism to “store” information in the time domain, as described further herein.

The traditional approach for storing time information as charge as illustrated in <figref idref="DRAWINGS">FIG. 2</figref> works very well in technologies that provide a large supply voltage VDD and for devices with long channel lengths to realize close to ideal current sources to charge the capacitor. However, scaling the circuit to short channel nodes is not trivial. Capacitor leakage in short channel technologies limits the “retention time” (t_ret) of voltage, which limits the maximum time-constant that is achievable in the system. For example, the traditional approach cannot be used to design digital PLLs that process phase information at low reference update rates (like 1 pps/1 Hz) that are required in network synchronization. In addition, using longer devices and capacitors requires significant area on chip—which is expensive in short channel process nodes. Advanced process technologies provide high precision in the time domain with small intrinsic gate delays owing to reduced parasitics and shorter channel lengths resulting in large transconductance g_m.

In order to store the time information, embodiments described herein leverage the high precision available in the time domain to “remember” the phase information as a pulse circulating in a delay line loop. <figref idref="DRAWINGS">FIGS. 8 and 9</figref> illustrate how the memory information may be supplied and saved as pulses circulating in a delay line rather than being used to turn on a current source as shown in <figref idref="DRAWINGS">FIG. 2</figref>. The XOR gate <b>801</b> creates a pulse <b>803</b> (shown as P_INin <figref idref="DRAWINGS">FIG. 9</figref>) having a width Δt when the rising edges of CLKIN and CLKREF occur at different times. CLKIN may be, e.g., CLKFB of <figref idref="DRAWINGS">FIG. 2</figref>. While the pulse may represent time information related to a phase difference between clock signals in a PLL, the pulse may more generally represent any time information between two events. The OR gate <b>805</b> receives the pulse <b>803</b> and supplies the pulse to a delay line <b>807</b>. The delay line is formed, e.g., by buffers or inverters. The delay line <b>807</b> feeds back its output to OR gate <b>805</b> to recirculate the pulses.

Referring to <figref idref="DRAWINGS">FIG. 9</figref>, the first pulse enters the delay line at <b>901</b> and exits the delay line as P_OUTat <b>903</b>. The output pulse is fed back as P_FBand reenters the delay line at <b>905</b>. That in turn results in pulse out at <b>907</b>. The pulse is recirculated until a reset signal <b>809</b> (<figref idref="DRAWINGS">FIG. 8</figref>) is asserted to reset the delay line, e.g., to force all the stages of the delay line to output a high or low voltage or an appropriate reset condition. Note the assumption that the maximum pulse width of Δt is less than the delay T_DLshown in <figref idref="DRAWINGS">FIG. 9</figref>.

<figref idref="DRAWINGS">FIG. 10</figref> shows an embodiment <b>1000</b> similar to the embodiment illustrated in <figref idref="DRAWINGS">FIG. 8</figref>. A conventional phase frequency detector <b>1001</b> supplies an UP pulse <b>1003</b> and a down (DN) pulse <b>1004</b>, which are logically combined in OR gate <b>1005</b>. OR gate <b>1005</b> supplies the input pulse P_INto a single delay line <b>1007</b> having a delay (T_DL). The delay line <b>1007</b> feeds back its output to OR gate <b>1005</b> to form a close-loop system that recirculates the pulses. The S-R latch <b>1011</b> generates the sign of Δt, based on the UP and DN pulses. A reset signal (RST) <b>1008</b> initializes the system and prepares the system for a next measurement. The delay line supplies the output signal to an AND gate <b>1009</b> that gates the pulses from delay line <b>1007</b>. For example, for a gain value of 5, the enable signal EN supplied by control logic (not shown) is asserted high to allow five pulses through AND gate <b>1009</b> and then de-asserted to gate off the pulses when not needed. The phase information from PFD <b>1001</b> is preserved as pulse Pout. Note that the approach of <figref idref="DRAWINGS">FIG. 10</figref> involves the least amount of hardware compared to later described embodiments but is sensitive to mismatch between propagation of rising and falling edges in the delay line.

<figref idref="DRAWINGS">FIG. 11</figref> illustrates an embodiment <b>1100</b> that desensitizes the circuit to delay mismatches between rising and falling edges in the delay line. The embodiment <b>1100</b> uses edge detectors <b>1101</b> and <b>1103</b> on the input pulse (P_IN), to generate two pulses corresponding to its rising (P_R) and falling (P_F) edges respectively. OR gates <b>1105</b> and <b>1107</b> receive the rising and falling edge pulses, respectively, and feed the pulses into two separate delay lines <b>1115</b> and <b>1117</b> with delays T_DL1and T_DL2. Thus, the rising and falling edge pulses circulating in the two delay lines represents the input pulse. The second input of each of the OR gates <b>1105</b> and <b>1107</b> is tied to the output of the corresponding delay line to form a close-loop system that recirculates the rising and falling edge pulses. Appropriate resets (not shown) are provided to initialize the system. Once initialized, the loop will regenerate the pulses over time. An SR latch <b>1119</b> receives the output of the delay lines <b>1115</b> and <b>1117</b> and reproduces the pulse supplied to the delay lines by OR gate <b>1109</b>. The “EN” signal for the output pulse (Pout), generated by a control block (not shown), allows through the number of pulses corresponding to the desired gain and gates off the pulses when not required. The time information (phase difference in the embodiment of <figref idref="DRAWINGS">FIG. 11</figref>) is preserved as the pulse width of P_INand P_OUT. The embodiment <b>1100</b> is sensitive to delay mismatch between the two delay lines and calibration can be used to correct any mismatch and ensure that T_DL1and T_DL2are equal.

<figref idref="DRAWINGS">FIG. 12</figref> illustrates another embodiment <b>1200</b> that alleviates the delay mismatch between the two delay lines shown in embodiment <b>1100</b> by using a single delay line <b>1207</b> to circulate both the rising edge and falling edge pulses. The embodiment illustrated in <figref idref="DRAWINGS">FIG. 12</figref> uses edge detectors <b>1201</b> and <b>1203</b> on the input pulse (P_IN) to generate two pulses corresponding to its rising (P_R) and falling (P_F) edges, respectively. OR gate <b>1205</b> receives the rising edge pulse and the falling edge pulse and supplies the pulses to the single delay line <b>1207</b> with delay (T_DL). The third input of OR gate <b>1205</b> is tied to the output of the delay line <b>1207</b> to form a close-loop system that recirculates the pulses. Appropriate resets (not shown) are provided to initialize the system. Once initialized, the loop will regenerate the pulses over time. A divide by two or toggle flip-flop <b>1209</b> receives the output of the delay line and reproduces the input pulse based on the rising and falling edge pulses. A control block (not shown) generates the “EN” signal for AND gate <b>1211</b> that supplies the output pulse (P_OUT), to provide an appropriate number of pulses corresponding to a desired gain and to gate-off the pulses when not required. The time (phase) information is preserved as pulse width of P_INand P_OUT.

<figref idref="DRAWINGS">FIG. 13</figref> illustrates an embodiment similar to that of <figref idref="DRAWINGS">FIG. 12</figref> with additional control to provide different delays for odd (rising) and even (falling) pulses. In certain cases, the pulse circulating through the delay line loop can diminish or even disappear because of asymmetric rising and falling edges. <figref idref="DRAWINGS">FIG. 13</figref> includes the edge detect circuit <b>1301</b> and <b>1303</b> similar in operation to <figref idref="DRAWINGS">FIG. 12</figref> and also includes a monostable multivibrator (also referred to herein as a mono-shot or one-shot). The monostable multivibrator <b>1351</b> in the feedback path regenerates a pulse with the same pulse width every time the pulse is re-circulated in the loop. Thus, the feedback signal of the delay line can come indirectly from the delay line in the form of the mono-shot pulse or directly from the output of the delay line as shown in, e.g., <figref idref="DRAWINGS">FIG. 8, 10, 11</figref>, or <b>12</b>. Use of the one-shot ensures that the pulse width doesn't become too small (≈0) or too large (≈T_DL) due to any systematic errors in the loop. The mono-shot affects both the rising edge pulse and falling edge pulse in the same way. The mono-shot “extends” the pulses (both the rising and falling edge pulses) by delaying one of the edges of the individual pulses. In other words, mono-shot ensures that the pulse width of each of the two pulses is restored to a constant value (“T_monoshot”). The actual information between two successive rising (or falling) edges of the pulses is not impacted by the mono-shot.

The embodiment also includes an optional fast delay path <b>1353</b> and slow delay path <b>1355</b> formed, e.g., by buffers, that can be used to adjust the pulse width. A multiplexer <b>1357</b> selects the fast delay path or the slow delay path based on a select signal from control logic. The control logic <b>1359</b> determines whether to increase the pulse or decrease the pulse width. For example, the control logic may increase the pulse width by delaying the falling edge pulse in the slow path <b>1355</b> while the rising edge pulse width uses the fast path <b>1353</b>. Alternatively, the control logic may decrease the pulse width by utilizing the slow path for the rising edge pulse and the fast path for the falling edge path. The control logic determines whether an edge is rising or falling based on whether it is odd or even.

The control logic <b>1359</b> that selects the fast or the slow path can be configured to “modulate” the pulse width in the loop. The actual operation depends on how the user wants the pulse width to change with time. Note that using this approach, the phase delay information can be made to be larger/smaller or monotonically increase/decrease by providing different delays in the feedback path. That can be used for noise shaping in a sigma delta loop.

For example, if the user wants the pulse width to monotonically increase, the control logic selects the “fast” path for the rising pulse and the “slow” path for the falling pulse. For that embodiment the control logic has a toggle flip-flop (not shown) clocked by the output of Div-by-2 <b>1358</b> to control the select line <b>1360</b> to the multiplexer <b>1357</b>. Such a control is useful in a pulse width modulation systems. Note that an extension of this control with a DTC (digital-to-time converter) can also be used to create a successive approximation register (SAR) TDC. In another embodiment, the control logic uses a pseudo-random bit sequence (PRBS) to randomize the selection of the fast/slow paths, which helps in mitigating spurs arising due to deterministic edges of the pulse for a given input.

<figref idref="DRAWINGS">FIG. 14</figref> illustrates an embodiment of an integrating fine TDC <b>1400</b> using three delay line elements <b>1402</b>. The pulse <b>1401</b> supplied by the pulse recirculating gain circuit controls a switch <b>1403</b>. When the pulse <b>1401</b> is asserted, the switch closes and power is supplied to the delay line <b>1405</b> causing a pulse to circulate in the delay line for the duration of the pulse <b>1401</b>. The circuit shown in <figref idref="DRAWINGS">FIG. 14</figref> is also known as a gated ring-oscillator (GRO). Here the ring oscillator continues to oscillate as long as the switch (<b>1403</b>) is closed by the pulse <b>1401</b> and freezes/stops when the switch is opened when the pulse is low. The number of pulses through the delay line <b>1405</b> is captured in counter <b>1407</b>. When the pulse <b>1401</b> de-asserts, the thermometer to binary (T2B) decoder <b>1409</b> supplies the value of each stage of the delay line as value X. Thus, the value determined is 3A+X for each pulse <b>1401</b>.

The multiplication by 3 can be understood as follows. Assume the number of times the GRO has “rolled over” is “A”, then the “effective” number of delay units that toggled during the time the switch (<b>1403</b>) was asserted is given by 3*A+X. Here the term 3*A corresponds to the total delay of “3” unit cells rolling over “A” times. To provide gain, the pulse recirculating gain circuit, examples of which are shown in <figref idref="DRAWINGS">FIGS. 8, 10, and 11-13</figref>, supplies pulse <b>1401</b> N times resulting in a gain of N or N(3A+X).

In embodiments, the initial state of the delay line can be arbitrary. That is, the GRO can start from any initial state (as long as it is recorded as the initial state). Starting from an arbitrary state works because the “final” output is taken as the difference of the final and the initial state (1^stdifference) in embodiments. See, e.g., <b>707</b> in <figref idref="DRAWINGS">FIG. 7</figref>. Note that this “barrel-shifting” operation provides 1^storder mismatch shaping for the delay mismatch between the units. The capacitors <b>1406</b> in delay line <b>1405</b> ensure that the next pulse <b>1401</b> to be integrated starts with the delay line <b>1405</b> in the same state as when it left off. That assumes that the next pulse from the recirculating delay line arrives before the capacitors have significantly discharged. The key is that the state of the GRO is “frozen” in between the N re-circulations. So the GRO “virtually” sees a pulse that is N times the input pulse width. The number of delay units <b>1403</b> is usually chosen to minimize the rollover frequency so that the number of rollovers (A) can be accurately captured using digital circuitry, which includes the counter and the thermometer to binary encoder. The number “<b>3</b>” shown in <figref idref="DRAWINGS">FIG. 14</figref> is for illustration. As mentioned above, the internal state of the GRO is frozen in between the conversions—in other words, the partial residue on the capacitors of the unit cells is assumed to be “held” before the next pulse from the recirculation arrives. That ensures that the GRO is operating as an integrating TDC, where integration is used to provide gain.

<figref idref="DRAWINGS">FIG. 15</figref> shows a high level block diagram of a TDC that uses a coarse TDC <b>1501</b> and a fine TDC <b>1503</b> that provides improved effective resolution using recirculation of input pulses as described above. The coarse TDC may be, e.g., a ripple counter. The fine TDC <b>1503</b> includes one of the recirculating delay lines described above in conjunction with an integrating delay line described, e.g., in <figref idref="DRAWINGS">FIG. 14</figref>. In the example of <figref idref="DRAWINGS">FIG. 15</figref>, the coarse TDC provides N coarse bits, e.g., 24 bits, and the fine TDC provides M bits, e.g., 8 fine bits.

Thus, various aspects have been described relating to improving the resolution of TDCs. The description of the invention set forth herein is illustrative, and is not intended to limit the scope of the invention as set forth in the following claims. Other variations and modifications of the embodiments disclosed herein, may be made based on the description set forth herein, without departing from the scope of the invention as set forth in the following claims.