The passive polyphase filter described in the paper is basically a network of resistor and capacitor elements. Therefore, it would be most straightforward to model the circuit using the corresponding 'resistor' and 'capacitor' primitives as shown in the below schematic (ppf_unit). Compared to other alternative modeling (e.g. using 'filter' primitives), this model can naturally describe the load effects between the stages when multiple polyphase filters are cascaded and any non-uniformity effects when mismatches among the element values are present.

The following testbench (tb_ppf1) drives the inputs in1 and in3 with two opposite phases of a 1GHz sinusoidal signal while grounding the remaining inputs in2 and in4, and observes the four output signals produced by the polyphase filter. The resistance parameter (R) and capacitance parameter (C) of the polyphase filter model are set to 1kΩ and 160fF, respectively, in order to set the resonant frequency of the network 1/(2𝛑RC) at 1GHz. The paper says that a single polyphase filter can produce the quadrature signals with equal amplitudes only at the vicinity of this resonant frequency.

The simulated waveforms of the four output signals are shown below when the input frequency is at 1.0GHz, 0.8GHz, and 1.2GHz, respectively. When the input frequency is equal to the resonant frequency of the polyphase filter of 1.0GHz, the equal-amplitude signals with the phases of 0, 90°, 180°, and 270° are produced, as explained by the paper. However, when the input frequency is different from the resonant frequency, the in-phase signals (0 and 180°) and quadrature-phase signals (90° and 270°) have different amplitudes.

To let the polyphase filter produce equal-amplitude outputs over a wider frequency range, one can cascade multiple stages of polyphase filters, as shown in the testbench below (tb_ppf2). The first polyphase filter has R=1kΩ and C=200fF, setting its resonant frequency at 0.8GHz, and the second polyphase filter has R=1kΩ and C=130fF, setting its resonant frequency at 1.2GHz. The paper provides the analysis saying that the overall polyphase filter can produce exactly equal-amplitude outputs at the two resonant frequencies, and if the spacing between the two frequencies is small enough, the amplitude differences within the range between the two resonant frequencies can be reasonably small.

The simulated waveforms from this second testbench confirm that it is true. For all the three input frequencies of 1.0GHz, 0.8GHz, and 1.2GHz, the 4-phase output signals have almost equal amplitudes. To extend the frequency range or reduce the amplitude difference further, one can add more polyphase filter stages. For example, another testbench (tb_ppf3) included in the attached package cascades 3 stages.

It is noteworthy that for this RC filter network propagating sinusoidal signals, XMODEL only had to process a single event at time 0. Hence, the run time is fast regardless of how long the simulation duration is.

Attachment: polyphase_filter_20220930.tar.gz

The passive polyphase filter described in the paper is basically a network of resistor and capacitor elements. Therefore, it would be most straightforward to model the circuit using the corresponding 'resistor' and 'capacitor' primitives as shown in the below schematic (ppf_unit). Compared to other alternative modeling (e.g. using 'filter' primitives), this model can naturally describe the load effects between the stages when multiple polyphase filters are cascaded and any non-uniformity effects when mismatches among the element values are present.

The following testbench (tb_ppf1) drives the inputs in1 and in3 with two opposite phases of a 1GHz sinusoidal signal while grounding the remaining inputs in2 and in4, and observes the four output signals produced by the polyphase filter. The resistance parameter (R) and capacitance parameter (C) of the polyphase filter model are set to 1kΩ and 160fF, respectively, in order to set the resonant frequency of the network 1/(2𝛑RC) at 1GHz. The paper says that a single polyphase filter can produce the quadrature signals with equal amplitudes only at the vicinity of this resonant frequency.

The simulated waveforms of the four output signals are shown below when the input frequency is at 1.0GHz, 0.8GHz, and 1.2GHz, respectively. When the input frequency is equal to the resonant frequency of the polyphase filter of 1.0GHz, the equal-amplitude signals with the phases of 0, 90°, 180°, and 270° are produced, as explained by the paper. However, when the input frequency is different from the resonant frequency, the in-phase signals (0 and 180°) and quadrature-phase signals (90° and 270°) have different amplitudes.

To let the polyphase filter produce equal-amplitude outputs over a wider frequency range, one can cascade multiple stages of polyphase filters, as shown in the testbench below (tb_ppf2). The first polyphase filter has R=1kΩ and C=200fF, setting its resonant frequency at 0.8GHz, and the second polyphase filter has R=1kΩ and C=130fF, setting its resonant frequency at 1.2GHz. The paper provides the analysis saying that the overall polyphase filter can produce exactly equal-amplitude outputs at the two resonant frequencies, and if the spacing between the two frequencies is small enough, the amplitude differences within the range between the two resonant frequencies can be reasonably small.

The simulated waveforms from this second testbench confirm that it is true. For all the three input frequencies of 1.0GHz, 0.8GHz, and 1.2GHz, the 4-phase output signals have almost equal amplitudes. To extend the frequency range or reduce the amplitude difference further, one can add more polyphase filter stages. For example, another testbench (tb_ppf3) included in the attached package cascades 3 stages.

It is noteworthy that for this RC filter network propagating sinusoidal signals, XMODEL only had to process a single event at time 0. Hence, the run time is fast regardless of how long the simulation duration is.

Attachment: polyphase_filter_20220930.tar.gz