# Exact meaning of 3db bandwidth?

M

#### Mike Noone

Jan 1, 1970
0
Hi - I recently came across the term "3db bandwidth" used in a way
which I was not entirely familiar. I am most familiar with the term
when used with amplifiers. For example, say in a FET amplifier where
you know that the midband gain [in db] = 20 * log(midband gain [in
V/V]), and the 3db bandwidth is the frequency which gives you a gain of
3db less than the midband gain.

Where I'm seeing it is in the datasheet for a gyro - the Analog

Can somebody please explain what exactly it means in this context?
Thanks!

-Mike

P

#### PeteS

Jan 1, 1970
0
Mike said:
Hi - I recently came across the term "3db bandwidth" used in a way
which I was not entirely familiar. I am most familiar with the term
when used with amplifiers. For example, say in a FET amplifier where
you know that the midband gain [in db] = 20 * log(midband gain [in
V/V]), and the 3db bandwidth is the frequency which gives you a gain of
3db less than the midband gain.

Where I'm seeing it is in the datasheet for a gyro - the Analog

Can somebody please explain what exactly it means in this context?
Thanks!

-Mike

Looking at the datasheet, it states:
-------
SETTING BANDWIDTH

External capacitors CMID and COUT are used in combination with on-chip
resistors to create two low-pass filters to limit the bandwidth of the
ADXRS401’s rate response. The –3 dB frequency set by ROUT and COUT is:

fOUT = 1/(2 x pi x Rout x Cout)
-----------

This is the standard -3dB point for a passive RC filter.

In this particular case, it refers to the rate of change OF the yaw rate
(2nd order differential) output. The rate output is specified as v being
proportional to rate (in degrees / sec) - i.e. a DC level for a constant
yaw rate. (My take, anyway)

HTH

Cheers

PeteS

M

#### [email protected]

Jan 1, 1970
0
Mike said:
Hi - I recently came across the term "3db bandwidth" used in a way
which I was not entirely familiar. I am most familiar with the term
when used with amplifiers. For example, say in a FET amplifier where
you know that the midband gain [in db] = 20 * log(midband gain [in
V/V]), and the 3db bandwidth is the frequency which gives you a gain of
3db less than the midband gain.

Where I'm seeing it is in the datasheet for a gyro - the Analog

Can somebody please explain what exactly it means in this context?
Thanks!

-Mike

3dB point of the low pass filter on page 9? come on dude. I suggest

M

#### [email protected]

Jan 1, 1970
0
Mike said:
Hi - I recently came across the term "3db bandwidth" used in a way
which I was not entirely familiar. I am most familiar with the term
when used with amplifiers. For example, say in a FET amplifier where
you know that the midband gain [in db] = 20 * log(midband gain [in
V/V]), and the 3db bandwidth is the frequency which gives you a gain of
3db less than the midband gain.

Where I'm seeing it is in the datasheet for a gyro - the Analog

Can somebody please explain what exactly it means in this context?
Thanks!

-Mike

The best way to understand RC filters is use ltspice. try this, save
as rc.asc or whatever.asc
and run in ltspice.

Version 4
SHEET 1 1072 680
WIRE -48 192 0 192
WIRE 0 192 0 208
WIRE -128 192 -208 192
WIRE 0 272 0 320
WIRE 0 192 64 192
WIRE -416 208 -416 176
WIRE -416 288 -416 304
WIRE 416 192 464 192
WIRE 464 192 464 208
WIRE 336 192 288 192
WIRE 464 272 464 320
WIRE 464 192 512 192
WIRE 832 192 880 192
WIRE 880 192 880 208
WIRE 752 192 704 192
WIRE 880 272 880 320
WIRE 880 192 960 192
FLAG 0 320 0
FLAG 64 192 Output1
FLAG -416 304 0
FLAG 464 320 0
FLAG 512 192 Output2
FLAG 880 320 0
FLAG 960 192 Output3
FLAG -416 176 ACin
FLAG -208 192 ACin
FLAG 288 192 ACin
FLAG 704 192 ACin
SYMBOL res -144 208 R270
WINDOW 0 32 56 VTop 0
WINDOW 3 0 56 VBottom 0
SYMATTR InstName R1
SYMATTR Value 1600
SYMBOL cap -16 208 R0
SYMATTR InstName C1
SYMATTR Value 10pF
SYMBOL voltage -416 192 R0
WINDOW 123 24 132 Left 0
WINDOW 39 0 0 Left 0
SYMATTR InstName V1
SYMATTR Value ""
SYMATTR Value2 AC 1
SYMBOL res 320 208 R270
WINDOW 0 32 56 VTop 0
WINDOW 3 0 56 VBottom 0
SYMATTR InstName R2
SYMATTR Value 806
SYMBOL cap 448 208 R0
SYMATTR InstName C2
SYMATTR Value 10pF
SYMBOL res 736 208 R270
WINDOW 0 32 56 VTop 0
WINDOW 3 0 56 VBottom 0
SYMATTR InstName R3
SYMATTR Value 1000
SYMBOL cap 864 208 R0
SYMATTR InstName C3
SYMATTR Value 10pF
TEXT -296 40 Left 0 !.ac dec 100 1000 10000e6

P

#### PeteS

Jan 1, 1970
0
Mike said:
Hi - I recently came across the term "3db bandwidth" used in a way
which I was not entirely familiar. I am most familiar with the term
when used with amplifiers. For example, say in a FET amplifier where
you know that the midband gain [in db] = 20 * log(midband gain [in
V/V]), and the 3db bandwidth is the frequency which gives you a gain of
3db less than the midband gain.

Where I'm seeing it is in the datasheet for a gyro - the Analog

Can somebody please explain what exactly it means in this context?
Thanks!

-Mike

The best way to understand RC filters is use ltspice. try this, save
as rc.asc or whatever.asc
and run in ltspice.

--------8<----------------- Snip

I think Mike understands filters, it's just the *way* the term was used
in this context was a bit different (which it is).

Cheers

PeteS

M

#### [email protected]

Jan 1, 1970
0
PeteS said:
Mike said:
Hi - I recently came across the term "3db bandwidth" used in a way
which I was not entirely familiar. I am most familiar with the term
when used with amplifiers. For example, say in a FET amplifier where
you know that the midband gain [in db] = 20 * log(midband gain [in
V/V]), and the 3db bandwidth is the frequency which gives you a gain of
3db less than the midband gain.

Where I'm seeing it is in the datasheet for a gyro - the Analog

Can somebody please explain what exactly it means in this context?
Thanks!

-Mike

The best way to understand RC filters is use ltspice. try this, save
as rc.asc or whatever.asc
and run in ltspice.

--------8<----------------- Snip

I think Mike understands filters, it's just the *way* the term was used
in this context was a bit different (which it is).

Cheers

PeteS

Lord, I appologize for that...that ain't right...and be with the
starvin' pygmies in New Guinea. Amen!"

T

#### Tim Wescott

Jan 1, 1970
0
Mike said:
Hi - I recently came across the term "3db bandwidth" used in a way
which I was not entirely familiar. I am most familiar with the term
when used with amplifiers. For example, say in a FET amplifier where
you know that the midband gain [in db] = 20 * log(midband gain [in
V/V]), and the 3db bandwidth is the frequency which gives you a gain of
3db less than the midband gain.

Where I'm seeing it is in the datasheet for a gyro - the Analog

Can somebody please explain what exactly it means in this context?
Thanks!

-Mike
Just the same as an amplifier.

The ideal gyro would give you an exact output (volts?) vs. rotation rate
input, no matter how fast the rotation rate was changing. Your gyro
will not do this. If you made a rate table that could impose a
sinusoidal rotation on the gyro at any frequency, you would find a point
where the output-to-input ratio was 0.707 the value that it is for a
constant rotation -- that's the 3dB point.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html

R

#### Ray

Jan 1, 1970
0
Mike said:
Hi - I recently came across the term "3db bandwidth" used in a way
which I was not entirely familiar. I am most familiar with the term
when used with amplifiers. For example, say in a FET amplifier where
you know that the midband gain [in db] = 20 * log(midband gain [in
V/V]), and the 3db bandwidth is the frequency which gives you a gain of
3db less than the midband gain.

Where I'm seeing it is in the datasheet for a gyro - the Analog

Can somebody please explain what exactly it means in this context?
Thanks!

-Mike
Just the same as an amplifier.

The ideal gyro would give you an exact output (volts?) vs. rotation rate
input, no matter how fast the rotation rate was changing. Your gyro
will not do this. If you made a rate table that could impose a
sinusoidal rotation on the gyro at any frequency, you would find a point
where the output-to-input ratio was 0.707 the value that it is for a
constant rotation -- that's the 3dB point.

Firstly, is the output measurement as a power or simple voltage?

If it is power (V^2), certainly 0.707 is the figure.
A simple voltage will however be 0.5.

I am certainly no expert on gyros, but I suspect in this instance we may
be dealing with a simple voltage, feedback and all that......

As the test apparatus is probably quite involved mechanically it may be
a tricky thing to verify I suspect.

a dB is actually defined as 10 log(test/ref) and is dimensionless, so it
can apply to any sort of measurement you care when comparing against a
known reference.

20 log (test/ref) really is a convenient way to perform POWER
measurements from a voltage reading, the V^2 is done in the log domain

Perhaps if I am only half correct in my reply, I'm 3dB out!

By all means, happy to be corrected if need be

Cheers, Ray

P

#### PeteS

Jan 1, 1970
0
Ray said:
Mike said:
Hi - I recently came across the term "3db bandwidth" used in a way
which I was not entirely familiar. I am most familiar with the term
when used with amplifiers. For example, say in a FET amplifier where
you know that the midband gain [in db] = 20 * log(midband gain [in
V/V]), and the 3db bandwidth is the frequency which gives you a gain of
3db less than the midband gain.

Where I'm seeing it is in the datasheet for a gyro - the Analog

Can somebody please explain what exactly it means in this context?
Thanks!

-Mike
Just the same as an amplifier.

The ideal gyro would give you an exact output (volts?) vs. rotation rate
input, no matter how fast the rotation rate was changing. Your gyro
will not do this. If you made a rate table that could impose a
sinusoidal rotation on the gyro at any frequency, you would find a point
where the output-to-input ratio was 0.707 the value that it is for a
constant rotation -- that's the 3dB point.

Firstly, is the output measurement as a power or simple voltage?

If it is power (V^2), certainly 0.707 is the figure.
A simple voltage will however be 0.5.

I am certainly no expert on gyros, but I suspect in this instance we may
be dealing with a simple voltage, feedback and all that......

As the test apparatus is probably quite involved mechanically it may be
a tricky thing to verify I suspect.

a dB is actually defined as 10 log(test/ref) and is dimensionless, so it
can apply to any sort of measurement you care when comparing against a
known reference.

20 log (test/ref) really is a convenient way to perform POWER
measurements from a voltage reading, the V^2 is done in the log domain

Perhaps if I am only half correct in my reply, I'm 3dB out!

By all means, happy to be corrected if need be

Cheers, Ray

The -3dB point is 0.5 Po/Pi, but 0.707 Vo/Vi for this sort of measurement.

0.5 Voltage (in dB) is -6dB

Cheers

PeteS

M

#### Mike Noone

Jan 1, 1970
0
PeteS said:
Looking at the datasheet, it states:
-------
SETTING BANDWIDTH

External capacitors CMID and COUT are used in combination with on-chip
resistors to create two low-pass filters to limit the bandwidth of the
ADXRS401's rate response. The -3 dB frequency set by ROUT and COUT is:

fOUT = 1/(2 x pi x Rout x Cout)
-----------

This is the standard -3dB point for a passive RC filter.

In this particular case, it refers to the rate of change OF the yaw rate
(2nd order differential) output. The rate output is specified as v being
proportional to rate (in degrees / sec) - i.e. a DC level for a constant
yaw rate. (My take, anyway)

HTH

Cheers

PeteS

Hi PeteS - that clears things up quite a bit. Thanks!

-Mike

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