I am building a Head-Amp for my Shure SE535. Can you give me a suggestion how to dimension C and R of the Zobel?
Depends on how much the amplifier needs it, really - there's a lot of things that play in here (even the choice of voltage gain affects stability margins). A simulation with halfway realistic models and capacitive loading may give more definitive answers.
PS: You'll find a good amount of Zobel-related discussion starting about here in this thread, including this interesting appnote.
Thank you for the links. Thats strange, no one have the link to Cherry's Paper about the Zobel.
How would you design the Zobel Network? Its for an Headphone amp with LT1010 as Buffe on the output.
How would you design the Zobel Network? Its for an Headphone amp with LT1010 as Buffe on the output.
But how would you dimension the C and R of the Zoble. I dont know the L of my headphone. And how to dimension it unversal, for a range of headphones?
I want to protect the OP from high frequency oscillating too. I dont see any suggestions how to calculate the R and C of the zobel in the links you posted.
I want to protect the OP from high frequency oscillating too. I dont see any suggestions how to calculate the R and C of the zobel in the links you posted.
Actually it's all about stability. It's essentially a control theory exercise, so some background in this can't hurt when trying to gain an understanding for the issue.
The part you are interested in is the effective output inductance of the amplifier, not the headphones'. Effective output L is a result of natural open-loop gain decrease (due to finite gain bandwidth) + open-loop output impedance. It will tend to form an LC resonator with load capacitance, with the expected phase shift that degrades amplifier phase margin. This is what the Zobel can push out to higher frequencies by inserting a zero in the transfer function.
The factors affecting effective output L very much depend on amplifier construction, including topology, part and current choices, supply bypassing, choice of closed-loop voltage gain, and circuit board layout.
I would shoot for stability into at least 10 nF of load capacitance (by simulation or experimentally). R is usually chosen to be in the vicinity of the load, so you could give something like 22...33 ohms a shot. Then you can pick C such that 1/(2 pi RC) = 300...500 kHz or so and see where that gets you.
The part you are interested in is the effective output inductance of the amplifier, not the headphones'. Effective output L is a result of natural open-loop gain decrease (due to finite gain bandwidth) + open-loop output impedance. It will tend to form an LC resonator with load capacitance, with the expected phase shift that degrades amplifier phase margin. This is what the Zobel can push out to higher frequencies by inserting a zero in the transfer function.
The factors affecting effective output L very much depend on amplifier construction, including topology, part and current choices, supply bypassing, choice of closed-loop voltage gain, and circuit board layout.
I would shoot for stability into at least 10 nF of load capacitance (by simulation or experimentally). R is usually chosen to be in the vicinity of the load, so you could give something like 22...33 ohms a shot. Then you can pick C such that 1/(2 pi RC) = 300...500 kHz or so and see where that gets you.
Stability 101: Driving a Capacitive Load (Operational Amplifiers)
https://www.youtube.com/watch?v=QHIninAg4Is
https://www.youtube.com/watch?v=QHIninAg4Is
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< ~1 nf is a better estimate for headphone cables which are short, although the desire for flexibility often means very thin insulation between strands
series Z output inductor||R or ferrite bead can be fine by itself without the Zobel shunt network
for higher Z headphones often just series R is used to isolate the C load from the feedback amplifier output
a shortcut for the analysis is if the open loop output Z of the amp is plotted in the datasheet, still resistive near the loop gain intercept frequency, then you can use the R value with the cable C estimate or measurement to get an estimate of added phase shift
datasheets also often give peaking/stability vs C load
series Z output inductor||R or ferrite bead can be fine by itself without the Zobel shunt network
for higher Z headphones often just series R is used to isolate the C load from the feedback amplifier output
a shortcut for the analysis is if the open loop output Z of the amp is plotted in the datasheet, still resistive near the loop gain intercept frequency, then you can use the R value with the cable C estimate or measurement to get an estimate of added phase shift
datasheets also often give peaking/stability vs C load
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it also good to look at the headphone specs -
SE535
Transducer type
Triple balanced-armature drivers
Sensitivity (at 1khz)
119 dB SPL/mW
Impedance (at 1kHz)
36 Ohm
this means to get to ~120 dB peak SPL the SE535 only needs ~ 280 mV peak, 7.7 mA peak
a 10:1 transformer pair would match it to modern consumer digital audio 2 Vrms fs line level output without any amplifier at all
SE535
Transducer type
Triple balanced-armature drivers
Sensitivity (at 1khz)
119 dB SPL/mW
Impedance (at 1kHz)
36 Ohm
this means to get to ~120 dB peak SPL the SE535 only needs ~ 280 mV peak, 7.7 mA peak
a 10:1 transformer pair would match it to modern consumer digital audio 2 Vrms fs line level output without any amplifier at all
wrong Zobel application - that article is for flattening speaker terminal Z
the LT1010 spice model does show some output Z behavior - but shouldn't be trusted exclusively
a 100 MHz scope and function gen plus a few test C in the lab are recommended
LT1010 input Zobel resistive termination would improve the output phase shift/Cload peaking and stability if driven from typical op amp buffered source which may have its output Z peaking where the LT1010 is reflecting Cload on its output as negative impedance at its input pin
the LT1010 spice model does show some output Z behavior - but shouldn't be trusted exclusively
a 100 MHz scope and function gen plus a few test C in the lab are recommended
LT1010 input Zobel resistive termination would improve the output phase shift/Cload peaking and stability if driven from typical op amp buffered source which may have its output Z peaking where the LT1010 is reflecting Cload on its output as negative impedance at its input pin
I suggest including the parasitics of the components in the feedback path. I add 10 nH in series with all resistors to cover leads and routing inductance and 2 pF in parallel with the R+L to cover the trace capacitance and end-to-end capacitance on the resistors.
I've measured the parasitics of leaded metal film resistors on an impedance analyzer (HP4194A). 10 nH is about right. The end-to-end cap is about 100 fF, but you easily pick up a 1 pF here and there in the PCB layout. 2 pF is probably a tad pessimistic, but in the right ballpark.
Include those parasitic components and watch the loop gain in the 1-10 MHz region. Then add the Zobel. The effect on stability is usually rather obvious.
~Tom
I've measured the parasitics of leaded metal film resistors on an impedance analyzer (HP4194A). 10 nH is about right. The end-to-end cap is about 100 fF, but you easily pick up a 1 pF here and there in the PCB layout. 2 pF is probably a tad pessimistic, but in the right ballpark.
Include those parasitic components and watch the loop gain in the 1-10 MHz region. Then add the Zobel. The effect on stability is usually rather obvious.
~Tom
input Zobel in dotted box, 2 uH lossy ferrite bead series Z gets shorted out by R3 with the .step command to compare
tested with simple loop gain test - can see unacceptable 10 degree phase margin improved with bead to 56 degrees
and again with i1 AC current applied to the LT1010 output - clear reduction in output Z peaking with lossy bead
principle is still the same even if LT1010 is used open loop - use a series inductor||R to isolate the Cload of the headphone cable from the LT1010 output
tested with simple loop gain test - can see unacceptable 10 degree phase margin improved with bead to 56 degrees
and again with i1 AC current applied to the LT1010 output - clear reduction in output Z peaking with lossy bead
principle is still the same even if LT1010 is used open loop - use a series inductor||R to isolate the Cload of the headphone cable from the LT1010 output
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