The current implementation allows selecting one out of seven integrator and resonator types, each of them providing their individuel set of parameters. Depending on the chosen type, the tool offers different design goals and constraints. Moreover, the selection affects the available settings in the D/A converter and coefficient blocks.
| Model Type | Integrator/Resonator model type. |
| Dynamics | Optimize for a defined minimum and maximum integrator output swing. |
| DC gain | DC Gain of the integrator/resonator.. |
| GBW/Bandwidth | Represents the GBW or location of the first pole depeding on the model type. |
| Resonance Frequency | Resonance Frequency if supported by the model. |
| Prop. path | High-level coefficient representing a proportional path, if supported by the model. |
Ideal integrator means, the integrator is ideal by all matters. There are no limitations in DC gain, GWB, etc. Each ideal integrator represents one state in the state-space model of the overal modulator model, which is used for optimization. A circuit-level model is shown in the figure below. Here, the circuit-level model utilizes an ideal OpAmp with a transfer characteristic of \(A(s)= \infty\). Feedback paths of the modulator are represented by the ideal current source with \(V_j\) as input.
In the OpAmp based integrator model, the dominant pole of the OpAmp is accounted for in order to investigate the most dominant non-ideal behavior. By this pole, finite DC gain and finite GBW can be modeled. Each OpAmp based integrator represents two states in the state-space model of the overal modulator model, which is used for optimization, obviously leading to smaller simulation throughputs than the ideal models. The model supports resistive and capacitive inputs represented by \(V_i\) and \(V_k\) in the circuit-level diagram below. Feedback paths of the modulator are represented by the ideal current source with \(V_j\) as input. During the optimization gain errors due to multiple resistive inputs are accounted for automatically.
As in the OpAmp based integrator model without proportional path, the dominant pole of the OpAmp is accounted for in order to investigate the most dominant non-ideal behavior. By this pole, finite DC gain and finite GBW can be modeled. Also each OpAmp based integrator with proportional path represents two states in the state-space model of the overal modulator model, which is used for optimization, obviously leading to smaller simulation throughputs than the ideal models. The proportional path is formed by the risistor \(R_p\). During the optimization gain errors due to multiple resistive inputs are accounted for automatically. The model is implemented as shown below in the circuit-diagram. Therefore, possible resonators feed back not only the integrated but also the proportionally scaled signal. The model supports resistive inputs represented by \(V_i\) in the circuit-level diagram below. Feedback paths of the modulator are represented by the ideal current source with \(V_j\) as input.
As an alternative, an OTA based integrator model is available. Each input path is formed by its own OTA with input voltage \(V_i\) and the frequency dependant gain \(g_\mathrm{m}(s)\), which shows one-pole behaviour. The pole location specifies the bandwidth of the OTA. A finite output transconductance is accounted by \(g_\mathrm{out}\). The model is implemented as shown below in the circuit-diagram. The model is represented in the state-space model of the overal modulator model by two states.
Ideal resonator means, the resonator is ideal by all matters. There are no limitations in DC gain, GWB, Q, etc. Each ideal resonator represents two states in the state-space model of the overal modulator model, which is used for optimization. A circuit-level model is shown in the figure below incorporating an LC resonator. Here, the circuit-level model utilizes an ideal OpAmp with a transfer characteristic of \(A(s)= \infty\). Feedback paths of the modulator are represented by the ideal current source with \(V_j\) as input.
In the OpAmp based resonator model, the dominant pole of the OpAmp is accounted for in order to investigate the most dominant non-ideal behavior. By this pole, finite DC gain and finite GBW can be modeled. Each OpAmp based resonator represents three states in the state-space model of the overal modulator model, which is used for optimization, obviously leading to smaller simulation throughputs than the ideal models. The model supports resistive inputs represented by \(V_i\) in the circuit-level diagram below. Feedback paths of the modulator are represented by the ideal current source with \(V_j\) as input. The finite resistance \(R_f\) is used to model a finite quality factor Q.
An OTA based resonator model is also available. Each input path is formed by its own OTA with input voltage \(V_i\) and the frequency dependant gain \(g_\mathrm{m}(s)\), which shows one-pole behaviour. The pole location specifies the bandwidth of the OTA. The output transconductance is \(g_\mathrm{out}\) used to model a finite quality factor Q. The model is implemented as shown below in the circuit-diagram. The model is represented in the state-space model of the overal modulator model by three states.
For each of the integrator and resonator models, an optimization goal for the output swing \(V_\mathrm{out}\) can be set. Modulators with swings lower than the \(V_\mathrm{out,min}\) or higher then the \(V_\mathrm{out,max}\) value are rated worse than ones within this boundaries.
Allows the genetic algorithm to change the DC gain in order to find a minimal acceptable value. This option enables the choice of \(A_\mathrm{DC,min}\) and \(A_\mathrm{DC,max}\) boundaries for a defined, allowed range.
Fixes the DC gain to a defined value during optimization. This option enables to choose the defined value in the range \(A_\mathrm{DC} \in [10;100000]\) on an absolute scale.
Low DC gain values will result in poor linearity, which is not investigated during the optimization!
Depending on the type of the non-ideal models, GBW or bandwidth are available as parameters. For OpAmp based models, GBW is used, for OTA based models bandwidth. Both \(f_\mathrm{gbw},f_\mathrm{b} \in [0.01;10]\) are normalized to \(f_\mathrm{s}\). Higher values than 10 times \(f_\mathrm{s}\) are considered as ideal and, thus, not supported. Both can be minimized or a fixed value can be set.
Allow the genetic algorithm to change \(f_\mathrm{gbw}/f_\mathrm{b}\) in order to find a minimal acceptable value. This option enables the choice of \(f_\mathrm{min}\) and \(f_\mathrm{max}\) boundaries for an allowed range.
Fixes \(f_\mathrm{gbw}/f_\mathrm{b}\) to a defined value during optimization.
For resonator models, the resonance frequency parameter \(f_0\) is shown. It is connected to the design goal that tries to place this frequency in the inband of the modulator. \(f_0\) is normalized to \(f_\mathrm{s}\).
Allow the genetic algorithm to change \(f_0\) in order to find an optimal value. This option enables the choice of \(f_\mathrm{min}\) and \(f_\mathrm{max}\) boundaries for an allowed range.
Fixes \(f_0\) to a defined value during optimization.
Optimize enables the genetic algorithm to change the value of this coefficient in order to find a better modulator. This option enables the choice of \(k_\mathrm{min}\) and \(k_\mathrm{max}\) boundaries for a defined, allowed range.
Fixes the coefficient \(k \in [0.00001;10)\) to a defined value during optimization.