Wien oscillator with real OPA – an easily derivation ...

Wien oscillator with real OPA – an easily derivation - Punčochář

K R

C

UW C

R

UO

Obr.1: Wien-bridge oscillator

Barkhausen: (1)

. (2) (3) (4) An ideal amplifier: K = K0

(5) If K0 = 3, then (6) Non ideal amplifier (7)

1

(8) (9) From the eq.(2) (10)

(11)

Ωr for Ω3 =15

Ωr for Ω3 = 50

[rad] 0,08

-

k

; Ω3 =15

k

; Ω3 =50

0,06 0,04 -

0,02 0 -0,02

0,9 90

0,95

1

1,05 05

1,1

Ω

-0,04 -0,06 -0,08

Obr. 2: Qualitative depiction of „phase“;

Thus it must be

(12) And (13) If we suppose 2

, thus

: ;

We can easily derive (14) For

(

if

) (15)

Rf Rg O Z Obr.3: K – a classical opa

(16) (17) If (18) (19) (20) For

is

. Thus (14a)

And an error 10% „we get“ if

and 1% if

!

The end  3