This example shows the bandwidth improvement that results from a cascode amplifier configuration (right-side circuit, light blue waveforms), compared to a single transistor amplifier configuration (left side, magenta waveforms).

In these circuits, identical transistor models are used. They are "datasheet" based behavioral models with typical small-signal NFET characteristics. This includes an internal Miller capacitance or Crss, which is set to 20 pF.

In the single transistor circuit, the Miller Theorem states that the effective value of Crss is increased by a factor of (1.0 + A), where A is the gain of the amplifier. In this case the factor is (1.0 + gfs * Rload), or 11x, so the effective Crss = 220 pF. Then the low-pass RC time constant of the input source resistance and the net input capacitance sets the amplifier bandwidth at just over 1 MHz.

For the cascode amplifier, the voltage at the drain of transistor m2 has very small variation, so the Miller effect is largely suppressed for that device. Transistor m3 amplifies these small voltage changes, but because the current in the Miller capacitance of m3 is drawn from the low impedance gate bias circuit, it does not limit the bandwidth of the amplifier.

You can move the probes around and look at the time-domain or frequency-domain signals at any point in the circuit, to gain more understanding of these component interactions.

This "Live" example design includes a simple analog electronic amplifier, intended only to demonstrates the importance of multi-discipline system modeling.

A swept frequency response test, from 40 Hz to 1000 Hz, shows the effect of the complex amplifier loading by the voice-coil and speaker-cone dynamics*. The electro-mechanical resonances strongly affect the current that must be supplied, in order to maintain a flat (controlled) output voltage over the specified frequency range. For example, the current in the voice-coil reaches a null at time 0.1 seconds, which corresponds to the effective "spring-mass" resonance frequency (60 Hz). The loudspeaker reaches its minimum impedance around 600 Hz, or at 0.6 seconds where the peak load current is observed.

The simulation results also show that the average power (q1/npn/pwr_avg) in the BDP947 BJT exceeds its 5 Watt rating across the entire range, but especially at lower frequencies. The red "hot part monitor", with the junction to ambient thermal resistance set to 10 C/Watt, as given in the datasheet, shows the part temperature rising to over 100 C. These diagnostic indicators make it obvious that we need a bigger transistor!

All of the parameters in blue can be changed by the user and a new simulation run. The updated scope waveform results will show the effect of that change. You can change the electrical resistance and inductance of the voice-coil, as well as the speaker cone mass and linear spring rate that affect the resonance frequency.

* Note: Please refer to this companion example, that shows the input impedance frequency response of the loudspeaker alone:

https://www.systemvision.com/design/loudspeaker-only-frequency-response

This example shows the bandwidth improvement that results from a cascode amplifier configuration (right-side circuit, light blue waveforms), compared to a single transistor amplifier configuration (left side, magenta waveforms).

In these circuits, identical transistor models are used. They are "datasheet" based behavioral models with typical small-signal NFET characteristics. This includes an internal Miller capacitance or Crss, which is set to 20 pF.

In the single transistor circuit, the Miller Theorem states that the effective value of Crss is increased by a factor of (1.0 + A), where A is the gain of the amplifier. In this case the factor is (1.0 + gfs * Rload), or 11x, so the effective Crss = 220 pF. Then the low-pass RC time constant of the input source resistance and the net input capacitance sets the amplifier bandwidth at just over 1 MHz.

For the cascode amplifier, the voltage at the drain of transistor m2 has very small variation, so the Miller effect is largely suppressed for that device. Transistor m3 amplifies these small voltage changes, but because the current in the Miller capacitance of m3 is drawn from the low impedance gate bias circuit, it does not limit the bandwidth of the amplifier.

You can move the probes around and look at the time-domain or frequency-domain signals at any point in the circuit, to gain more understanding of these component interactions.

This "Live" example design includes a simple analog electronic amplifier, intended only to demonstrates the importance of multi-discipline system modeling.

A swept frequency response test, from 40 Hz to 1000 Hz, shows the effect of the complex amplifier loading by the voice-coil and speaker-cone dynamics*. The electro-mechanical resonances strongly affect the current that must be supplied, in order to maintain a flat (controlled) output voltage over the specified frequency range. For example, the current in the voice-coil reaches a null at time 0.1 seconds, which corresponds to the effective "spring-mass" resonance frequency (60 Hz). The loudspeaker reaches its minimum impedance around 600 Hz, or at 0.6 seconds where the peak load current is observed.

The simulation results also show that the average power (q1/npn/pwr_avg) in the BDP947 BJT exceeds its 5 Watt rating across the entire range, but especially at lower frequencies. The red "hot part monitor", with the junction to ambient thermal resistance set to 10 C/Watt, as given in the datasheet, shows the part temperature rising to over 100 C. These diagnostic indicators make it obvious that we need a bigger transistor!

All of the parameters in blue can be changed by the user and a new simulation run. The updated scope waveform results will show the effect of that change. You can change the electrical resistance and inductance of the voice-coil, as well as the speaker cone mass and linear spring rate that affect the resonance frequency.

* Note: Please refer to this companion example, that shows the input impedance frequency response of the loudspeaker alone:

https://www.systemvision.com/design/loudspeaker-only-frequency-response

This "Live" example design includes a simple analog electronic amplifier, intended only to demonstrates the importance of multi-discipline system modeling.

A swept frequency response test, from 40 Hz to 1000 Hz, shows the effect of the complex amplifier loading by the voice-coil and speaker-cone dynamics*. The electro-mechanical resonances strongly affect the current that must be supplied, in order to maintain a flat (controlled) output voltage over the specified frequency range. For example, the current in the voice-coil reaches a null at time 0.1 seconds, which corresponds to the effective "spring-mass" resonance frequency (60 Hz). The loudspeaker reaches its minimum impedance around 600 Hz, or at 0.6 seconds where the peak load current is observed.

The simulation results also show that the average power (q1/npn/pwr_avg) in the BDP947 BJT exceeds its 5 Watt rating across the entire range, but especially at lower frequencies. The red "hot part monitor", with the junction to ambient thermal resistance set to 10 C/Watt, as given in the datasheet, shows the part temperature rising to over 100 C. These diagnostic indicators make it obvious that we need a bigger transistor!

All of the parameters in blue can be changed by the user and a new simulation run. The updated scope waveform results will show the effect of that change. You can change the electrical resistance and inductance of the voice-coil, as well as the speaker cone mass and linear spring rate that affect the resonance frequency.

* Note: Please refer to this companion example, that shows the input impedance frequency response of the loudspeaker alone:

https://www.systemvision.com/design/loudspeaker-only-frequency-response

This "Live" example design includes a simple analog electronic amplifier, intended only to demonstrates the importance of multi-discipline system modeling.

A swept frequency response test, from 40 Hz to 1000 Hz, shows the effect of the complex amplifier loading by the voice-coil and speaker-cone dynamics*. The electro-mechanical resonances strongly affect the current that must be supplied, in order to maintain a flat (controlled) output voltage over the specified frequency range. For example, the current in the voice-coil reaches a null at time 0.1 seconds, which corresponds to the effective "spring-mass" resonance frequency (60 Hz). The loudspeaker reaches its minimum impedance around 600 Hz, or at 0.6 seconds where the peak load current is observed.

The simulation results also show that the average power (q1/npn/pwr_avg) in the BDP947 BJT exceeds its 5 Watt rating across the entire range, but especially at lower frequencies. The red "hot part monitor", with the junction to ambient thermal resistance set to 10 C/Watt, as given in the datasheet, shows the part temperature rising to over 100 C. These diagnostic indicators make it obvious that we need a bigger transistor!

All of the parameters in blue can be changed by the user and a new simulation run. The updated scope waveform results will show the effect of that change. You can change the electrical resistance and inductance of the voice-coil, as well as the speaker cone mass and linear spring rate that affect the resonance frequency.

* Note: Please refer to this companion example, that shows the input impedance frequency response of the loudspeaker alone:

https://www.systemvision.com/design/loudspeaker-only-frequency-response

This "Live" example design includes a simple analog electronic amplifier, intended only to demonstrates the importance of multi-discipline system modeling.

A swept frequency response test, from 40 Hz to 1000 Hz, shows the effect of the complex amplifier loading by the voice-coil and speaker-cone dynamics*. The electro-mechanical resonances strongly affect the current that must be supplied, in order to maintain a flat (controlled) output voltage over the specified frequency range. For example, the current in the voice-coil reaches a null at time 0.1 seconds, which corresponds to the effective "spring-mass" resonance frequency (60 Hz). The loudspeaker reaches its minimum impedance around 600 Hz, or at 0.6 seconds where the peak load current is observed.

The simulation results also show that the average power (q1/npn/pwr_avg) in the BDP947 BJT exceeds its 5 Watt rating across the entire range, but especially at lower frequencies. The red "hot part monitor", with the junction to ambient thermal resistance set to 10 C/Watt, as given in the datasheet, shows the part temperature rising to over 100 C. These diagnostic indicators make it obvious that we need a bigger transistor!

All of the parameters in blue can be changed by the user and a new simulation run. The updated scope waveform results will show the effect of that change. You can change the electrical resistance and inductance of the voice-coil, as well as the speaker cone mass and linear spring rate that affect the resonance frequency.

* Note: Please refer to this companion example, that shows the input impedance frequency response of the loudspeaker alone:

https://www.systemvision.com/design/loudspeaker-only-frequency-response

This "Live" example design includes a simple analog electronic amplifier, intended only to demonstrates the importance of multi-discipline system modeling.

A swept frequency response test, from 40 Hz to 1000 Hz, shows the effect of the complex amplifier loading by the voice-coil and speaker-cone dynamics*. The electro-mechanical resonances strongly affect the current that must be supplied, in order to maintain a flat (controlled) output voltage over the specified frequency range. For example, the current in the voice-coil reaches a null at time 0.1 seconds, which corresponds to the effective "spring-mass" resonance frequency (60 Hz). The loudspeaker reaches its minimum impedance around 600 Hz, or at 0.6 seconds where the peak load current is observed.

The simulation results also show that the average power (q1/npn/pwr_avg) in the BDP947 BJT exceeds its 5 Watt rating across the entire range, but especially at lower frequencies. The red "hot part monitor", with the junction to ambient thermal resistance set to 10 C/Watt, as given in the datasheet, shows the part temperature rising to over 100 C. These diagnostic indicators make it obvious that we need a bigger transistor!

All of the parameters in blue can be changed by the user and a new simulation run. The updated scope waveform results will show the effect of that change. You can change the electrical resistance and inductance of the voice-coil, as well as the speaker cone mass and linear spring rate that affect the resonance frequency.

* Note: Please refer to this companion example, that shows the input impedance frequency response of the loudspeaker alone:

https://www.systemvision.com/design/loudspeaker-only-frequency-response

MOSFET common source amplifier using 2N7000