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Which cross-over frequency is this referring to with respect to the DC-DC Converter Switching frequency

It's more than likely referring to the the LC resonant frequency (\$f_c\$) of the energy storage components within the DC-to-DC converter. See L and C below: -

Cross over frequency should not be higher than 1/8th of switching frequency

The L and C form a low pass filter that below resonance, barely alter the phase angle between input (the switching waveform) and output (the smoothed DC voltage). However, as resonance (\$f_c\$) approaches, the phase changes dramatically from near 0° to 180°. That change of phase is unavoidable and can turn a stable circuit into an unstable oscillator. \$f_c\$ has to be some way below the switching frequency for it to be effective.

Simulation

Using an on-line simulator, consider L = 10 uH and C = 10 uF for the energy transfer components and, look at the green trace (phase response) below: -

Link to Interactive calculator

Slightly below \$f_c\$ =15.9 kHz (referred to as \$f_n\$ in the picture above), the phase shift is quite close to 0° and this poses no threat of introducing loop instability. However, slightly above 15.9 kHz, the phase has shifted nearly 180° and this can really "shake the ground" when it comes to stability. This is why compensation circuits are added within the PWM control block (see top picture) to retard the 180° phase shift and prevent this oscillatory condition arising. The compensation is a counter-measure to unwanted oscillation.

To achieve adequate filtering of switching voltages on the output, you need to keep the resonant frequency (\$f_c\$) of the energy transfer components (L and C) significantly below the switching frequency. The further you go below the switching frequency, the better the result i.e. lower output ripple voltage. The LC is a great low pass filter for this and, in the above picture, you can probably see that if the switching frequency were at 159 kHz (\$10\times f_c\$), the attenuation of the switching voltage will be 40 dB compared to DC. That's a 100:1 reduction

Example: if the switching is 10 volts p-p, the resulting 1st harmonic on the output waveform will be 100 times lower at 100 mV p-p. However, you also want to keep the resonant frequency high so that your closed-loop control system can react quickly to load and supply changes.

These two requirements are in opposition so a compromise is necessary.

Why 8:1? Why not 10:1? It's a rule of thumb and like most rules of thumb, you can choose to push the rule this way or that way depending on your most dominant needs.

Hopefully, the information above will allow you to see that the choice of LC cross-over frequency is a compromise based on juggling these somewhat opposing constraints: -

• Good loop response to load and supply voltage changes (\$f_c\$ needs to be high)
• Ensuring the compensation circuit is effective at the resonance (\$f_c\$ "right")
• Minimizing output ripple voltage (\$f_c\$ needs to be low)

Which cross-over frequency is this referring to with respect to the DC-DC Converter Switching frequency

It's more than likely referring to the the LC resonant frequency (\$f_c\$) of the energy storage components within the DC-to-DC converter. See L and C below: -

Cross over frequency should not be higher than 1/8th of switching frequency

The L and C form a low pass filter that below resonance, barely alter the phase angle between input (the switching waveform) and output (the smoothed DC voltage). However, as resonance (\$f_c\$) approaches, the phase changes dramatically from near 0° to 180°. That change of phase is unavoidable and can turn a stable circuit into an unstable oscillator. For the LC filtering to be effective, \$f_c\$ has to be some way below the switching frequency. The further below the switching frequency, the lower the output ripple amplitude.

Simulation

Using an on-line simulator, consider L = 10 uH and C = 10 uF for the energy transfer components and, look at the green trace (phase response) below: -

Link to Interactive calculator

Slightly below \$f_c\$ = 15.9 kHz (referred to as \$f_n\$ in the picture above), the phase shift is quite close to 0° and this poses no threat of introducing loop instability. However, slightly above 15.9 kHz, the phase has shifted nearly 180° and this can really "shake the ground" when it comes to stability. This is why compensation circuits are added within the PWM control block (see top picture) to retard the 180° phase shift and prevent this oscillatory condition arising. The compensation is a counter-measure to unwanted oscillation.

Low output ripple vs faster closed-loop control

To achieve adequate filtering of switching voltages on the output, you need to keep the resonant frequency (\$f_c\$) of the energy transfer components (L and C) significantly below the switching frequency. The further you go below the switching frequency, the better the result i.e. lower output ripple voltage. The LC is a great low pass filter for this and, in the above picture, you can probably see that if the switching frequency were at 159 kHz (\$10\times f_c\$), the attenuation of the switching voltage will be 40 dB compared to DC. That's a 100:1 reduction

Example: if the switching is 10 volts p-p, the resulting 1st harmonic on the output waveform will be 100 times lower at 100 mV p-p. However, you also want to keep the resonant frequency high so that your closed-loop control system can react quickly to load and supply changes.

These two requirements are in opposition so a compromise is necessary.

Why 8:1? Why not 10:1? It's a rule of thumb and like most rules of thumb, you can choose to push the rule this way or that way depending on your most dominant needs.

Hopefully, the information above will allow you to see that the choice of LC cross-over frequency is a compromise based on juggling these somewhat opposing constraints: -

• Good loop response to load and supply voltage changes (\$f_c\$ needs to be high)
• Ensuring the compensation circuit is effective at the resonance (\$f_c\$ "right")
• Minimizing output ripple voltage (\$f_c\$ needs to be low)

Which cross-over frequency is this referring to with respect to the DC-DC Converter Switching frequency

It's more than likely referring to the the LC resonant frequency (\$f_c\$) of the energy storage components within the DC-to-DC converter. See L and C below: -

The L and C form a low pass filter that below resonance (suggested as being one-eighth of the switching frequency in the question), barely alter the phase angle between input (the switching waveform) and output (the smoothed DC voltage). However, as resonance (\$f_c\$) approaches, the phase changes dramatically from near 0° to 180°. That change of phase is unavoidable and can turn a stable circuit into an unstable oscillator.

Using an on-line simulator, consider L = 10 uH and C = 10 uF for the energy transfer components and look at the green (phase) response below: -

Link to Interactive calculator

Slightly below 15.9 kHz (\$f_c\$ but referred to as \$f_n\$ in the picture), the phase shift is quite close to 0° and this poses no threat of causing loop instability. However, slightly above 15.9 kHz, the phase has shifted nearly 180° and this can really "shake the ground" when it comes to stability. This is why compensation circuits are added within the PWM control block (see top picture) to retard the 180° phase shift and prevent this oscillatory condition arising. The compensation is a counter-measure to unwanted oscillation.

To achieve adequate filtering of switching voltages on the output, you need to keep the resonant frequency (\$f_c\$) of the energy transfer components (L and C) significantly below the switching frequency. The further you go below the switching frequency, the better the result i.e. lower output ripple voltage. The LC is a great low pass filter for this and, in the above picture, you can probably see that if the switching frequency were at 159 kHz (\$10\times f_c\$), the attenuation of the switching voltage will be 40 dB compared to DC. That's a 100:1 reduction

Example: if the switching is 10 volts p-p, the resulting 1st harmonic on the output waveform will be 100 times lower at 100 mV p-p. However, you also want to keep the resonant frequency high so that your closed-loop control system can react quickly to load and supply changes.

These two requirements are in opposition so a compromise is necessary.

Why 8:1? Why not 10:1? It's a rule of thumb and like most rules of thumb, you can choose to push the rule this way or that way depending on your most dominant needs.

Hopefully, the information above will allow you to see that the choice of LC cross-over frequency is a compromise based on juggling these somewhat opposing constraints: -

• Good loop response to load and supply voltage changes (\$f_c\$ needs to be high)
• Ensuring the compensation circuit is effective at the resonance (\$f_c\$ "right")
• Minimizing output ripple voltage (\$f_c\$ needs to be low)

Which cross-over frequency is this referring to with respect to the DC-DC Converter Switching frequency

It's more than likely referring to the the LC resonant frequency (\$f_c\$) of the energy storage components within the DC-to-DC converter. See L and C below: -

Cross over frequency should not be higher than 1/8th of switching frequency

The L and C form a low pass filter that below resonance, barely alter the phase angle between input (the switching waveform) and output (the smoothed DC voltage). However, as resonance (\$f_c\$) approaches, the phase changes dramatically from near 0° to 180°. That change of phase is unavoidable and can turn a stable circuit into an unstable oscillator. \$f_c\$ has to be some way below the switching frequency for it to be effective.

Simulation

Using an on-line simulator, consider L = 10 uH and C = 10 uF for the energy transfer components and, look at the green trace (phase response) below: -

Link to Interactive calculator

Slightly below \$f_c\$ =15.9 kHz (referred to as \$f_n\$ in the picture above), the phase shift is quite close to 0° and this poses no threat of introducing loop instability. However, slightly above 15.9 kHz, the phase has shifted nearly 180° and this can really "shake the ground" when it comes to stability. This is why compensation circuits are added within the PWM control block (see top picture) to retard the 180° phase shift and prevent this oscillatory condition arising. The compensation is a counter-measure to unwanted oscillation.

To achieve adequate filtering of switching voltages on the output, you need to keep the resonant frequency (\$f_c\$) of the energy transfer components (L and C) significantly below the switching frequency. The further you go below the switching frequency, the better the result i.e. lower output ripple voltage. The LC is a great low pass filter for this and, in the above picture, you can probably see that if the switching frequency were at 159 kHz (\$10\times f_c\$), the attenuation of the switching voltage will be 40 dB compared to DC. That's a 100:1 reduction

Example: if the switching is 10 volts p-p, the resulting 1st harmonic on the output waveform will be 100 times lower at 100 mV p-p. However, you also want to keep the resonant frequency high so that your closed-loop control system can react quickly to load and supply changes.

These two requirements are in opposition so a compromise is necessary.

Why 8:1? Why not 10:1? It's a rule of thumb and like most rules of thumb, you can choose to push the rule this way or that way depending on your most dominant needs.

Hopefully, the information above will allow you to see that the choice of LC cross-over frequency is a compromise based on juggling these somewhat opposing constraints: -

• Good loop response to load and supply voltage changes (\$f_c\$ needs to be high)
• Ensuring the compensation circuit is effective at the resonance (\$f_c\$ "right")
• Minimizing output ripple voltage (\$f_c\$ needs to be low)

It's more than likely referring to the the LC resonant frequency of the energy storage components within the DC-to-DC converter. It likely refers to these because below the "so-called" cross-over frequency, the LC circuit does not introduce significant phase shift within the loop (a good thing).

  However, above the cross-over frequency there is virtually a total phase inversion due to the LC changing its characteristic rapidly. Consider 10 uH and 10 uF for the energy transfer components and look at the green (phase) response below: -

Slightly below 15.9 kHz, the phase shift is quite close to 0° and this poses no threat of causing loop instability. However, slightly above 15.9 kHz, the phase has shifted nearly 180° and this can really "shake the ground" when it comes to stability. This is why compensation circuits are added within the control loop to advance the phase shift (a counter measure) and prevent the 180° oscillatory condition arising.

So, as a "guide", you keep the resonant frequency of the energy transfer components significantly below the switching frequency. But, you also need to keep that resonant frequency high to avoid the 180° phase shift occurring at too low a frequency; you don't want it to occur at a frequency where the "compensation" isn't active.

You also want to keep the resonant frequency high so that your closed-loop control system can react quickly to load and supply changes.

But there's also another criteria to consider and that is the output ripple voltage.

You need to keep the resonant frequency a decent way below the switching frequency so that switching artefacts are kept to an acceptably low level on the output waveform. The LC is a great low pass filter for this and, in the above picture, you can probably see that if the switching frequency were 159 kHz, the attenuation of the switching voltage will be 40 dB compared to DC. So, if the switching is 10 volts p-p, the resulting 1st harmonic on the output waveform will be 100 times lower at 100 mV p-p.

But you can probably also see that if the switching frequency were only slightly above the LC resonant frequency that there could be ripple artefact amplification and this is to be totally avoided because it wrecks the output voltage quality.

Why 8:1? Why not 10:1? The fact is, that it's a rule of thumb and like most rules of thumb, you can choose to push the rule this way or that way depending on your most dominant needs.

• Good loop response to load and supply voltage changes (Fc wants to be high)
• Ensuring the compensation circuit is effective at the resonance (Fc "right")
• Minimizing output ripple voltage (Fc needs to be low)

It's more than likely referring to the the LC resonant frequency (\$f_c\$) of the energy storage components within the DC-to-DC converter. See L and C below: -

The L and C form a low pass filter that below resonance (suggested as being one-eighth of the switching frequency in the question), barely alter the phase angle between input (the switching waveform) and output (the smoothed DC voltage). However, as resonance (\$f_c\$) approaches, the phase changes dramatically from near 0° to 180°. That change of phase is unavoidable and can turn a stable circuit into an unstable oscillator.

Using an on-line simulator, consider L = 10 uH and C = 10 uF for the energy transfer components and look at the green (phase) response below: -

Slightly below 15.9 kHz (\$f_c\$ but referred to as \$f_n\$ in the picture), the phase shift is quite close to 0° and this poses no threat of causing loop instability. However, slightly above 15.9 kHz, the phase has shifted nearly 180° and this can really "shake the ground" when it comes to stability. This is why compensation circuits are added within the PWM control block (see top picture) to retard the 180° phase shift and prevent this oscillatory condition arising. The compensation is a counter-measure to unwanted oscillation.

To achieve adequate filtering of switching voltages on the output, you need to keep the resonant frequency (\$f_c\$) of the energy transfer components (L and C) significantly below the switching frequency. The further you go below the switching frequency, the better the result i.e. lower output ripple voltage. The LC is a great low pass filter for this and, in the above picture, you can probably see that if the switching frequency were at 159 kHz (\$10\times f_c\$), the attenuation of the switching voltage will be 40 dB compared to DC. That's a 100:1 reduction

Example: if the switching is 10 volts p-p, the resulting 1st harmonic on the output waveform will be 100 times lower at 100 mV p-p. However, you also want to keep the resonant frequency high so that your closed-loop control system can react quickly to load and supply changes.

These two requirements are in opposition so a compromise is necessary.

Why 8:1? Why not 10:1? It's a rule of thumb and like most rules of thumb, you can choose to push the rule this way or that way depending on your most dominant needs.

• Good loop response to load and supply voltage changes (\$f_c\$ needs to be high)
• Ensuring the compensation circuit is effective at the resonance (\$f_c\$ "right")
• Minimizing output ripple voltage (\$f_c\$ needs to be low)