IF.455K: Gain Vs Stable

@6/20 2012

try to  figure out how  the "old" low tech IF amplifier works  and  what it provide.  here is the practical parts i ever tried in debugging IF-B0 .

Vcc=11V~12V

Component:  BJT  2sc9018 (ss9018)

The  Hybrid-pi model is used to routhly design the LC tuned load IF amplifer.

for 2sc9018(or ss9018, they are almost same characters ):

        * β = 120                    (*which we are going to used)

        * Rπ = 26(mA)/Ie*β 

        * Va >=74V                (*Early voltage roughly Calculate  from FIg.2 @Ie<5mA,60V, from Spice Model Vaf=74V   )

         *Ro = (Va + Vce)/Ie  ~= 28K  (@Ie=3mA, 168k@0.5mA)                    


Fig.2

Fig.3



Popular IFT on Chian Taobao

TTF-1-1 36+127:10,  Q>=80               

TTF-1-2  RED: 36+127:8   Q>=80

TTF-1-3 yellow  139+25:11

TTF-2-1 : 45+117:7 , Q=80-120     

 TTF-2-2: 45+117: 10, Q=80-120

TTF-2-9: 48+114:25, Q=80-120

My stock IFT on hand

primary: 

                  primary:  134.21 uH

                  primary tap-top:   89.447uH

                  primary tap-bottom:: 4.39uH

                  seconday: 0.1020H

Pri:Sec = sqrt(134.21/0.1020)   ~=  36:1

Tap:primary= sqrt(134.21/4.39)  ~=  5.5:1

 yellow IF.T.:

               Primary:402.7660 uH

               Seconday:2.4462 uH

p:s = sqrt(402.766/2.4462) = 12.8:1

red coil:(NOT transformer)

                 2.3405uH default

                 max: 2.9784  2.9788 2.9777

                 min:  1.9965   1.9943

                 system error:  0.0230



big pink IFT:

     primary: 4.3320uH

     tap-top: 1.246uH

     tap-bottom: 1.1989uH

   secondary: 0.064uH

  Primary:Secondary=sqrt(4.332/0.064) ~= 8:1

  tap: 1.9:1

IF-B0 gain analysis

Rt=2.pi.f.L.Q ( the impedance of the  tuned LC circuit)

Rp: total impedance in the primary of transformer

IF frequency: 465kHz

IFT characters

T1[yellow IFT]: primary: 350uH, 300pF, primary 6.3ohm Q ~=90 [calculated 150,practically, around 80-100, not by testing]

 p:s =  12.8:1

Rt=Xl*Q = 2 * pi * f * L*Q =2*3.1415926*465*10^3*350*10^-6*90 ~=90k

T2(tap green IFT): primary 760pF, 134uH, 3ohm,Q=90 (practically, use Q=80-100 as estimation)

      P:S= 36:1

      tap = 5.5:1 (primary: tap)

      Rt=Xl*Q =  2 * pi * f * L*Q= 2*3.1415926*465*10^3*136*10^-6*140 ~=35k

Stage 1 gain

T1 secondary load: 126*(26/3mA)*12.8*12.8 ~= 178.9k

Q1 output resistance:  27k

total T1 load: Rp= 28K | 178.9 | 165 = 21K

gain of stage1: 20*log((2mA/26)*18.77k/12.8)= 42dB (insert loss around 3dB)

Qload = Rp/(2*pi*f*L) = 18

Bw=f.res /Q = 25kHz


Stage 2 gain

Rt=35k,  P:S= 36:1,    tap = 5.5:1 (primary: tap)

T2 secondary load: 300R*36*36 = 388.8K (300R ,the estimation of detector input impedance )

Q 1 output resistance: 24K

total T1 load: { 28k|| 388.8k/(5.5*5.5)=12.85k || 35k/(5.5*5.5)= 1.934k } ~= 1k

Gain of stage1: 20*log(3mA/26*1k*5.5/36) = 24dB

total gain:  44dB + 24dB-5dB ~= 70dB


stage 2 change to IFT TF2-9  (48+114: 25)

600uH, 200pF, 465khz,  Q=100

p:s = 6.48:1

p:tap = 3.37:1

Rt=Xl*Q = 2 * pi * f * L*Q =2*3.1415926*465*10^3*600*10^-6*100 ~=175k

T2 secondary load: 300R*6.48*6.48 = 12.6K

Q 1 output resistance: 24K

total T1 load: { 24k|| 12.6/(3.37*3.37)=1.1k || 175k/(3.37*3.37)= 15k } = 1k

Gain of stage1: 20*log(3mA/26*1k*3.37/6.48) = 35dB

total gain:  44dB + 35dB-5dB ~= 75dB


Change to TF-1-3 yellow  139+25:11

600uH, 200pF, 465khz,  Q=80

p:s =14.9:1

tap = 5.56

colector:Sec=2.27

Rt=Xl*Q = 2 * pi * f * L*Q =2*3.1415926*465*10^3*600*10^-6*100 ~=140k

T2 secondary load: 300R*6.48*6.48 = 66K

Q 1 output resistance: 24K

total T1 load: { 24k|| 12.6/(5.56*5.56)=2.1k || 175k/(3.37*3.37)= 15k } = 1.7k

Gain of stage1: 20*log(3mA/26*1.7k*5.56/14.9) = 37dB

total gain:  44dB + 37dB-5dB ~= 76dB



IF-B0 : Stable Margin estimation

IF Stage stable constrain

A stable amplifier,  gm, Rb, Rc limited by :

2*pi*f*c*gm*RbRc < 2   

[refer to <<Principles of Transistor Circuits>>  Ninth Edition@2000  Appendix C]

To provide a stable UN-neutralization amplifier, need margin factor 4,  So 

2*pi*f*c*gm*RbRc = 2/4 = 0.5

f: IF frequncy in HZ                     c: in Fala                 

Rb: the impedance which ideal amplifier see from it's input

Rc: the impedance which ideal amplifier see from it's output

Suppose Stages BJT's base impedance just the stage's input impedance(@update 2012/12/11, this is wrong,  in normal case the BJT base see the impedance domain by the pre-stage's  loaded tank's Rt) Then,

@455khz, c(Cob)=1.7pF(9018),  gm=Ie/26, input resistance: Rb=beta*(26/Ie)    Ie: mA

Rc*Rb <= 0.5/(2*pi*f*c*gm)= 0.5/(2*pi*f*c*(Ie/26)))  

               = 2.67*10^6/Ie

9018 IF Stage stable constrain

9018 IF sage stable conditions (Rc,Rb: in Kohm, Ie in mA , IF=455kHz, c=1.7pF )  [@updated 2012/12/11]

Rc*Rb*Ie<=2.67    (stable factor n=4)

Rc*Rb*Ie<=10.68  ( start oscillation)

stable margin of stage 2 :the IFT TF2-9  (48+114: 25)    @2012/12/11

--------------------------------------------------------------------------------

600uH, 200pF, 465khz,  Q=100

p:s = 6.48:1

p:tap = 3.37:1

Rt=Xl*Q = 2 * pi * f * L*Q =2*3.1415926*465*10^3*600*10^-6*100 ~=175k

Rc=detector||(Rt/3.37/3.37)|| ro=28k ~=1kohm

(detector ~=300*6.48*6.48/3.37/3.37)

Rb= first stage Rt || BJT-Rin~=  600R ||  (100*26/0.5) = 600R

test result: Ie from 1mA to 10mA get gain from 25dB to 45dB, be stable.

@3mA, Ie=3mA,Rc=1k,  Rb=0.6K , Gain=20*log(Rc*Ie/26/1.7) = 35dB

stable constrained:  Rc*Rb*Ie=0.6*1*3 = 1.8 < 2.67

@10mA Ie=10mA,  Rc=1k, Rb=0.6k,   Gain=20*log(Rc*10/26/1.7) = 46dB

stable constrained:  Rc*Rb*Ie =1*0.6*10 = 6  >= 2.7, stable factor dropped to 1.7

Why oscillation in my first trying use IFT 

@2012/12/11

p:s =  12.8:1,Q ~=90 , Rt=90k

3mA BJT-Ro = 44k

Rb= first stage Rt || BJT-Rin= (90k/12.8/12.8) ||  (100*26/0.5) = 0.6k

Rc= Rt|| Detector Impedance|| BJT-Ro = 90k||(300*12.8*12.8)  || 44k ~= 18K

(Ie~=3mA)

if Ie use 2.7mA as first designed

Rb*Rc*Ie =18×0.6x2.7 = 29, far away from stable!!!!(STABLE SHOULD < 10/n)