CN112468142B - Fractional frequency multiplication injection locking oscillator working method based on multipoint injection technology - Google Patents
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Abstract
The invention relates to the technical field of injection locking oscillators, in particular to a fractional frequency multiplication injection locking oscillator working method based on a multipoint injection technology, which comprises the steps of achieving fine change of an equivalent injection position by using a variable-strength and multipoint injection mode, because the multi-point simultaneous injection meets the equivalent vector superposition characteristic, the equivalent injection intensity and injection position are realized by gradually selecting the injection position and changing the proportion of the injection intensity of each point, the fractional frequency multiplication is to be realized, the core of the method is that the current injection position is changed by fraction times of 2 pi radian compared with the last injection position, the method utilizes the characteristic that signals injected at multiple points in the ring oscillator simultaneously meet the vector superposition, the fine change of the position of the injection signal is achieved through the change of the injection position and the strength of the injection signal, and therefore the injection locking oscillator with fractional frequency multiplication capacity is achieved.
Description
Technical Field
The invention relates to the technical field of injection locking oscillators, in particular to a fractional frequency multiplication injection locking oscillator working method based on a multipoint injection technology.
Background
The frequency multiplication structure based on the injection locking technology is widely applied to injection locking oscillators, injection locking phase-locked loops and the like due to the excellent phase noise performance of the frequency multiplication structure. However, the injection-locked frequency multiplication structure was only applicable to the reference frequency f REF Integral multiple of (i.e. output frequency of N x f) REF (N ═ 1,2,3, …), the output frequency accuracy (i.e., the step size of the change) is limited to f REF 。
Several techniques are known in the art in an attempt to solve the above-mentioned problems. Some of these techniques are listed below:
1. by using multiple phases of the ring oscillator, 1/2 times and 1/4 times f are achieved REF The frequency resolution of (a). (see, e.g., the article "An indexed emission-locked PLL with1/2-and 1/4-integral subcircuric locking in 90nm CMOS," in IEEE Radio Frequency integrated Circuits Symposium,2012, pp.189-192 of S.Lee et al.
2. This Sequential Injection Locking (SIL) to achieve 1/N times f by sequentially injecting on each node around an N-stage ring oscillator REF The frequency resolution of (a). (see P.park et al article "all-digital clock generator using a reactive injection-locked oscillator in 65nm CMOS," in IEEE int.solid-State Circuits Conf.Dig.Tech.papers,2012, pp.336-337.
3. The sum and difference modulator is used to randomize the injection of selected delay cells to achieve a refined frequency resolution. (see K. -H.Teng et al article "A370-pJ/b multichannel BFSK/QPSK transmitter using injection-locked fractional-N synthesizer for wireless biotechnologies," IEEE J.solid-State Circuits, vol.52, No.6, pp.867-880, Mar.2017.
In 3, there is a quantization phase noise problem of high frequency shaping in the sequential injection locking structure based on the sum and difference modulator. These techniques attempt to solve this problem:
4. the high frequency shaped quantization phase noise is reduced by increasing the injection signal frequency and decreasing the injection signal strength after the sum and difference modulator is used. (see W.Deng et al "A0.048 mm) 2 3mW synthesizable fractional-N PLL with a soft injection-locking technique,”in IEEE Int.Solid-State Circuits Conf.Dig.Tech.Papers,2015,pp.252–253。
5. After the sum and difference modulator is used, by adding a Phase Locked Loop (PLL) at the next stage. (see X.Meng et al, "A low-noise digital-to-frequency converted on injection-locking oscillator and random phase selection for fractional-Nfrequency synthesis," IEEE transactions.on Very Large Scale Integration (VLSI) Systems, vol.27, No.6, pp.1578-1389, Jun.2019.
The traditional injection locking oscillator can only realize integer frequency multiplication, and the precision of output frequency is limited. To achieve fractional frequency multiplication, the technique described in item 2 can be used, and this way of sequential injection locking can achieve 1/N times f REF The frequency resolution of (a). However, to achieve better resolution, the number of delay cell stages must be increased. To take into account the outputThe expression for the frequency is:
wherein T is inv The delay time of a single-stage delay unit is adopted, so that the output frequency is reduced due to the increase of N, and the power consumption is increased due to the increase of the number of stages, so that the real requirement cannot be met;
when the technique described in the second item 3 is used, the sum-difference modulator may additionally introduce shaped quantization noise, which significantly deteriorates the noise performance at the high frequency offset of the output signal;
although the second terms 4 and 5 are trying to solve the high frequency quantization noise introduced by the sum and difference modulator, 4 sacrifices the noise performance, and 5 may generate folded phase noise or fractional spurs due to the defects of the charge pump.
The multi-point injection technology with programmable intensity provided by the invention can even realize higher frequency resolution without using a sum-difference modulator, thereby avoiding the problems.
The invention aims to break through the limitation of the number of oscillator stages to the accuracy of the output frequency under the condition of not using a sum-difference modulator. And fine variation of the injection position is equivalently realized by using the multi-point injection technology by utilizing the characteristic that the injection signals can be vector-superposed. Thereby, a higher target frequency, a high precision frequency resolution, and an excellent phase noise performance can be obtained.
Disclosure of Invention
The invention aims to overcome the problems in the prior art and provides a fractional frequency multiplication injection locking oscillator working method based on a multipoint injection technology, which can solve the problems in the prior art at least to a certain extent.
In order to achieve the technical purpose and achieve the technical effect, the invention is realized by the following technical scheme:
a fractional frequency multiplication injection locking oscillator working method based on a multipoint injection technology comprises the following steps:
step 1) achieving fine change of equivalent injection positions by using a variable-strength and multi-point injection mode, wherein due to the fact that signals injected at the same time at multiple points meet equivalent vector superposition characteristics in an oscillator, required injection strength and injection positions are equivalently achieved by gradually selecting injection positions and changing the injection strength of each point;
step 2) based on the vector superposition characteristics satisfied by multipoint injection in step 1), realizing fine change of an equivalent injection position and equivalent injection strength which is kept unchanged, and realizing fractional frequency multiplication in a sequential injection locked oscillator, wherein the core is that the current injection position is changed by 2 pi radian compared with the last injection position, the output frequency precision is improved by M times under the condition of not increasing the number N of ring oscillator stages, and the effect required to be achieved is that the phase shift generated by each injection position is 2 pi/(M × N) compared with the previous injection position;
step 3) realizing the digital controllability of the injection signal intensity, adjusting the injection intensity by utilizing the number of gating injection transistors in a pseudo-differential oscillation unit, changing the injection intensity by integral multiple unit intensity compared with the last injection when realizing each described injection, inserting mu injection pipes between every two delay stages by cascading N stages of delay units, and selectively accessing or completely cutting off the injection signal by each injection pipe through an alternative data selector so as to achieve the adjustability of each injection intensity mu +1 stage;
step 4) determining the injection position and the injection intensity corresponding to the injection position by using a circuit structure of a digital programmable mode, wherein the circuit comprises a plurality of groups of counters, a pulse circuit generator, a plurality of multipath output selectors and a binary code to thermometer code converter circuit, and the working method specifically comprises the following contents:
step 4.1, reference clock signal f REF The accumulator carries out accumulation once at each rising edge moment through the a-bit accumulator, the accumulated result x corresponds to the injection intensity of the second point when two points are injected, and the injection intensity of the first point is 2 a X, i.e. the injection intensity per point is 2 a The +1 level is adjustable, and the total injection intensity of two points is always 2 a The output of the accumulator is passedDecoding after a multi-channel output selector to gate the number of injection transistors;
step 4.2, reference clock signal f REF Generating a pulse signal with a period consistent with that of a reference source signal and a certain pulse width through a pulse generating module, using the pulse signal as an injection signal, and outputting the pulse signal to a phase to be injected through a multi-path output selector;
step 4.3, taking an overflow signal of the a-bit accumulator as a counting signal of the b-bit counter, and adding 1 to a counting result of the b-bit counter every time the a-bit accumulator overflows;
step 4.4, the counting result of the b-bit counter is accessed into the multi-path output selector as an address signal, the counting result of the counter corresponds to two adjacent phases of the current injection, namely, the injection position can be from phi along with each overflow of the a-bit accumulator 0 、Φ 1 Becomes phi 1 、Φ 2 From Φ 1 、Φ 2 Becomes phi 2 、Φ 3 … …, from Φ N-2 、Φ N-1 Becomes phi N-1 、Φ 0 Achieving the effect of sequential injection locking;
step 4.5, if the injection locking frequency multiplier with the minimum frequency resolution is to be realized, the injection position and the injection intensity are as follows in sequence: phi 0 Place strobe 2 a +1 injection tubes, phi 1 Gate 0 injection tubes → phi 0 Place strobe 2 a A filling pipe phi 1 Gate 1 injection tube → phi 0 Place strobe 2 a -1 injection tube,. phi 1 Gate 2 injection tubes → … … → phi 0 Gate 1 injection tube, phi 1 Place strobe 2 a Injection tube → phi 0 Gate 0 injection tubes phi 1 Place strobe 2 a +1 injection tubes, phi 2 Gate 0 injection tubes → phi 1 Place strobe 2 a A filling pipe phi 2 Gate 1 injection tube → … …;
wherein each "→" represents one time f REF The rising edge of (a) of (b),
the injection sequence is periodically and circularly carried out, so that the minimum frequency resolution can be realized
Further, in the step 3), when the number of the gate injection transistors is used to change the injection strength, the following contents are specifically included: using single-ended delay cells with independently programmable injection strength Str < 1 > … Str < M > as selection signal to determine injection signal I through one-out-of-two data selector nj If Str is equal to 1, the transistor injection behavior is indicated, and the number of thermometer codes 1 also determines the injection strength, and if the number of Str < 1 > … Str < M > is equal to 1, the injection strength is n.
The invention has the beneficial effects that: the characteristic that signals injected at multiple points in the ring oscillator simultaneously meet vector superposition is utilized, and the fine change of the position of the injected signal is achieved through the change of the injection position and the strength of the injected signal, so that the injection locking oscillator with fractional frequency multiplication capacity is realized, and the specific benefits are as follows:
1. in a structure without using a sum-difference modulator (DSM), the output frequency accuracy of the conventional structure depends on the number of oscillator stages, but when the number of stages is increased to improve the output accuracy, the oscillation frequency of the oscillator is reduced;
2. when the sum-difference modulator is used to achieve good output precision, shaping quantization noise is introduced, and the noise performance of a high-frequency offset part of an output signal is obviously deteriorated;
3. the invention utilizes the characteristic that the injection signals can be subjected to vector superposition, uses the multi-point injection technology to realize the fine change of the injection position, breaks through the limitation of the number of the oscillator stages on the output frequency precision under the condition of not using a sum-difference modulator, thereby obtaining higher target frequency and high-precision frequency resolution and simultaneously keeping excellent phase noise performance.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the description below are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic block diagram of a conventional sequential injection locked ring oscillator and a sum and difference modulator based sequential injection locked ring oscillator;
FIG. 2(a) is a schematic diagram of injection position changes in a conventional sequential injection lock; FIG. 2(b) is a schematic diagram of injection position change in sequential injection lock based on a sum-difference modulator;
FIG. 3 is a schematic diagram of the application of a multi-point (two-point) injection locking technique in a ring oscillator;
FIG. 4 is a schematic diagram of the fine variation of the equivalent injection position achieved in a 2-stage differential ring oscillator by a multi-point (two-point) injection technique;
FIG. 5 is a schematic diagram of a delay cell with independently programmable implant strengths according to an embodiment of the present invention;
FIG. 6 is a schematic diagram of a ring oscillator for implementing a multi-point, variable strength injection locked in accordance with an embodiment of the present invention;
fig. 7 is a schematic structural diagram of a control circuit for determining an injection position and an injection intensity corresponding to the injection position in the embodiment of the present invention.
Detailed Description
In order to make the technical means, the creation characteristics, the achievement purposes and the effects of the invention easy to understand, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, but not all the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
A fractional frequency multiplication injection locking oscillator working method based on a multipoint injection technology comprises the following steps:
step 1) achieving fine change of equivalent injection positions by using a variable-strength and multi-point injection mode, wherein due to the fact that signals injected at the same time at multiple points meet equivalent vector superposition characteristics in an oscillator, required injection strength and injection positions are equivalently achieved by gradually selecting injection positions and changing the injection strength of each point;
step 2) based on the vector superposition characteristics satisfied by multipoint injection in step 1), realizing fine change of an equivalent injection position and equivalent injection strength which is kept unchanged, and realizing fractional frequency multiplication in a sequential injection locked oscillator, wherein the core is that the current injection position is changed by 2 pi radian compared with the last injection position, the output frequency precision is improved by M times under the condition of not increasing the number N of ring oscillator stages, and the effect required to be achieved is that the phase shift generated by each injection position is 2 pi/(M × N) compared with the previous injection position;
step 3) realizing the digital controllability of the intensity of the injection signal, utilizing the number of gating injection transistors to adjust the injection intensity in a pseudo-differential oscillation unit, and realizing that the integral multiple unit intensity is changed compared with the injection intensity of unit intensity changed by last injection when the injection is performed each time, inserting mu injection pipes between every two delay stages by cascading N-stage delay units, wherein each injection pipe is selectively accessed to the injection signal or completely switched off by an alternative data selector, thereby achieving the adjustability of each injection intensity mu +1 stage;
step 4) determining the injection position and the injection intensity corresponding to the injection position by using a circuit structure of a digital programmable mode, wherein the circuit comprises a plurality of groups of counters, a pulse circuit generator, a plurality of multipath output selectors and a binary code to thermometer code converter circuit, and the working method specifically comprises the following contents:
step 4.1, reference clock signal f REF The accumulator carries out accumulation once at each rising edge moment through the a-bit accumulator, the accumulated result x corresponds to the injection intensity of the second point when two points are injected, and the injection intensity of the first point is 2 a X, i.e. the injection intensity per point is 2 a The +1 level is adjustable, and the total injection intensity of two points is alwaysIs 2 a The output of the accumulator is decoded after passing through a multi-output selector, and the number of the injection transistors is gated;
step 4.2, reference clock signal f REF Generating a pulse signal with a certain pulse width and a period consistent with those of a reference source signal through a pulse generating module, using the pulse signal as an injection signal, and outputting the pulse signal to a phase to be injected through a multi-path output selector;
step 4.3, taking an overflow signal of the a-bit accumulator as a counting signal of the b-bit counter, and adding 1 to a counting result of the b-bit counter every time the a-bit accumulator overflows;
step 4.4, the counting result of the b-bit counter is accessed into the multi-path output selector as an address signal, the counting result of the counter corresponds to two adjacent phases of the current injection, namely, the injection position can be from phi along with each overflow of the a-bit accumulator 0 、Φ 1 Becomes phi 1 、Φ 2 From Φ 1 、Φ 2 Becomes phi 2 、Φ 3 … …, from Φ N-2 、Φ N-1 Becomes phi N-1 、Φ 0 Achieving the effect of sequential injection locking;
step 4.5, if the injection locking frequency multiplier with the minimum frequency resolution is to be realized, the injection position and the injection intensity are as follows in sequence: phi (phi) of 0 Place strobe 2 a +1 injection tubes, phi 1 Gate 0 injection tubes → phi 0 Place strobe 2 a Injection pipe phi 1 Gate 1 injection tube → phi 0 Place strobe 2 a -1 injection tube,. phi 1 Gate 2 injection tubes → … … → phi 0 Gate 1 injection tube, phi 1 Place strobe 2 a Injection tube → phi 0 Gate 0 injection tubes phi 1 Place strobe 2 a +1 injection tubes, phi 2 Where the gate gates 0 injection pipes (where the a-bit accumulator has 1 overflow) → Φ 1 Place strobe 2 a Injection pipe phi 2 Gate 1 injection tube → … …;
wherein each "→" represents one time f REF The rising edge of (a) of (b),
the injection sequence is periodically and circularly carried out, so that the minimum frequency resolution is realized
Further, in the step 3), when the number of the gate injection transistors is used to change the injection strength, the following contents are specifically included: using single-ended delay cells with independently programmable injection strength Str < 1 > … Str < M > as selection signal to determine injection signal I through one-out-of-two data selector nj If Str is equal to 1, the transistor injection behavior is indicated, meanwhile, the number of thermometer codes with1 also determines the injection intensity, and if the number of Str < 1 > … Str < m > equal to 1 is n, the injection intensity is n.
In fig. 1, when the input of the accumulator is 1, the overall structure is a conventional sequential injection locked ring oscillator, and the injection positions are as shown in fig. 2(a), i.e., the position of each injection is changed to 1 phase compared to the previous injection — for an N-level ring oscillator, the change amount of each injection position is 2 pi/N, and after N periods of reference source, the race of 2 pi radians is completed, so that the reference source frequency with the precision of 1/N times is output;
in fig. 1, when the input of the accumulator is Δ Σ M output, the overall structure is a sequential injection locked ring oscillator based on a sum-difference modulator, and the injection positions are as shown in fig. 2(b), that is, the positions of each injection are changed to α phases as compared with the previous injection on average over a plurality of cycles — for an N-level ring oscillator, the amount of change of each injection position is 2 π α/N, and after N/α reference source cycles, chase of 2 π radians is completed, so that the reference source frequency with the accuracy of α/N times is output;
however, the sum-difference modulator is designed to control the number of outputs 0 and 1 to achieve an average value α, rather than a fraction of the true output α, and thus introduces a quantization noise problem.
FIG. 3 is a schematic diagram of the application of a multi-point (two-point) injection locking technique in a ring oscillator, where the injection location and injection strength of the equivalent injection signal are derived from the actual vector superposition of the two injection signals when both injection signals are present simultaneously;
fig. 4 is a schematic diagram of implementing fine variation of equivalent injection position in a 2-stage differential ring oscillator by multi-point (two-point) injection technique — by changing the injection signal strength of two adjacent points and sequentially selecting two injection points, the position of each injection can be changed to 1/3 phase compared to the position of the last injection, and the output accuracy of 1/12 reference source frequency is achieved, and if conventional sequential injection locking is applied, the accuracy is only 1/4 reference source frequency;
FIG. 5 is a schematic diagram of a delay cell structure with independently programmable implant intensities determined by the number of gated implant transistors, such that the variation of the implant intensities is linearly controllable, in accordance with an embodiment of the present invention;
fig. 6 is a schematic diagram of an embodiment of the present invention for implementing a multi-point and variable-strength injection locked ring oscillator, where the delay unit structure is the same as that in fig. 5, and the schematic diagram selects 8-level differences (16 phases), and the injection strength is adjustable by 8 steps, so that the output frequency accuracy, i.e., the number of phases and the number of injection strength steps, of 1/(16 × 8) times of the reference source frequency can be adjusted according to practical applications;
fig. 7 is a schematic diagram of a control circuit for determining an injection position and an injection strength corresponding to the injection position according to an embodiment of the present invention, wherein the number of bits of the accumulator is determined by the number of injection strength steps, and the number of bits of the counter is determined by the number of phases of the ring oscillator.
It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in the process, method, article, or apparatus that comprises the element.
The preferred embodiments of the invention disclosed above are intended to be illustrative only. The preferred embodiments are not intended to be exhaustive or to limit the invention to the precise embodiments disclosed. Obviously, many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the invention and the practical application, to thereby enable others skilled in the art to best utilize the invention. The invention is limited only by the claims and their full scope and equivalents.
Claims (2)
1. A fractional frequency multiplication injection locking oscillator working method based on a multipoint injection technology is characterized by comprising the following steps:
step 1) achieving fine change of equivalent injection positions by using a variable-strength and multi-point injection mode, wherein due to the fact that signals injected at the same time at multiple points meet equivalent vector superposition characteristics in an oscillator, required injection strength and injection positions are equivalently achieved by gradually selecting injection positions and changing the injection strength of each point;
step 2) based on the vector superposition characteristic satisfied by multipoint injection in step 1), realizing fine change of an equivalent injection position and equivalent injection strength which is kept unchanged, and realizing fractional frequency multiplication in a sequential injection locked oscillator, wherein the core of the method is that the current injection position generates 2 pi radian change compared with the last injection position, the output frequency precision is improved by M times under the condition of not increasing the stage number N of the ring oscillator, and the effect required to be achieved is to ensure that the phase shift of each injection position compared with the previous injection position is 2 pi/(M x N);
step 3) realizing the digital controllability of the intensity of the injection signal, utilizing the number of gating injection transistors to adjust the injection intensity in a pseudo-differential oscillation unit, changing the injection intensity by integral multiple unit intensity compared with the injection intensity of the last time when realizing the described each injection, cascading N stages of delay units, inserting M injection pipes between every two delay stages, and selectively accessing or completely shutting off the injection signal by an alternative data selector for each injection pipe so as to achieve the adjustability of each injection intensity M +1 stage;
step 4) determining the injection position and the injection intensity corresponding to the injection position by using a circuit structure of a digital programmable mode, wherein the circuit comprises a plurality of groups of counters, a pulse circuit generator, a plurality of multipath output selectors and a binary code to thermometer code converter circuit, and the working method specifically comprises the following contents:
step 4.1, reference clock signal f REF The accumulator carries out accumulation once at each rising edge moment through the a-bit accumulator, the accumulated result x corresponds to the injection intensity of the second point when two points are injected, and the injection intensity of the first point is 2 a X, i.e. the injection intensity per point is 2 a The +1 level is adjustable, and the total injection intensity of two points is always 2 a The output of the accumulator is decoded after passing through a multi-path output selector, and the number of the injection transistors is gated;
step 4.2, reference clock signal f REF Generating a pulse signal with a period consistent with that of a reference source signal and a certain pulse width through a pulse generating module, using the pulse signal as an injection signal, and outputting the pulse signal to a phase to be injected through a multi-path output selector;
step 4.3, taking an overflow signal of the a-bit accumulator as a counting signal of the b-bit counter, and adding 1 to a counting result of the b-bit counter every time the a-bit accumulator overflows;
step 4.4, the counting result of the b-bit counter is accessed into the multi-path output selector as an address signal, the counting result of the counter corresponds to two adjacent phases of the current injection, namely, the injection position can be from phi along with each overflow of the a-bit accumulator 0 、Φ 1 Becomes phi 1 、Φ 2 From Φ 1 、Φ 2 Becomes phi 2 、Φ 3 … …, from Φ N-2 、Φ N-1 Becomes phi N-1 、Φ 0 Achieving the effect of sequential injection locking;
step 4.5, if the injection locking frequency multiplier with the minimum frequency resolution is to be realized, the injection position and the injection intensity are as follows in sequence: phi 0 Place strobe 2 a +1 injection tubes, phi 1 Gate 0 injection tubes → phi 0 Place strobe 2 a A filling pipe phi 1 Gate 1 injection tube → phi 0 Place strobe 2 a -1 injection tube,. phi 1 Gate 2 injection tubes → … … → phi 0 Gate 1 injection tube, phi 1 Place strobe 2 a Injection tube → phi 0 Gate 0 injection tubes phi 1 Place strobe 2 a +1 injection tubes, phi 2 Gate 0 injection tubes → phi 1 Place strobe 2 a A filling pipe phi 2 Gate 1 injection tube → … …;
wherein each "→" represents one time f REF The rising edge of (a) of (b),
the injection sequence is periodically and circularly carried out, so that the minimum frequency resolution is realized
2. The operating method of fractional frequency doubling injection locked oscillator based on multi-point injection technology according to claim 1, wherein in the step 3), when the injection strength is changed by using the number of gated injection transistors, the method specifically includes the following steps: using single-ended delay cells with independently programmable injection strengths Str < 1 > … Str < M > as selection signals through an alternative data selector to determine injection signal I nj If Str is equal to 1, the transistor injection behavior is indicated, and the number of thermometer codes 1 also determines the injection strength, and if the number of Str < 1 > … Str < M > is equal to 1, the injection strength is n.
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