VOLTAGE-TO-FREQUENCY CONVERTER

VOLTAGE-TO-FREQUENCY CONVERTER

Internal circuit of LM331 IC S R Q Q

+

+

+

VOLTAGE REFERENCE +Vcc +Vi n +Vcc +Vcc +Vcc F_out

LM331

Q1 Q2 Q3 Q4 Q5 Q6 1 2 3 15 R 2R R1 R1 1,89V R_S R_L C_L R_T C_T R_P VOLT COMP VOLT COMP OP AMP CURRENT MIRROR

ONE SHOT TIMER

2 1 6 7 8 5 4 3 R_B I_S I_S

In direct transmission of an analog signal (below), V_AN will be more easily corrupted by noise.

IN TERFA C E TEM PERA T URE

SEN SO R

V

_AN SIGN A L

+

N O ISE SIGN A L

FILT ER

V

_AN

By converting VAN to a large signal whose frequency is proportional to VAN, the transmission of the signal

becomes much less corruptible by external noise.

TEM PERA T URE SEN SO R IN TERFA C E V to F CO N V ERTER FIL T ER -LEV EL DECTECTO R F to V CO N V ERTER

V

_AN

V

_AN SIG N A L

+

N O ISE SIGN A L

Timing Diagram V in V_CL=V₆ I₁ V_CT=V₅ I_S 0 0 0 2/3 V _cc FIXED PW VARIABLE SW 1,1C_TR_T Tout -1,1C_TR_T V ave m+= I s-(Vave/RL) C _L m- = V_ave R_L C_L ∆V_CL initial transient charging C _L from 0 to V _in+∆V_L V out V cc 0 m+= I s C_L V cc SET RESET RIPPLE VOLTAGE

The DC current, or average current, through capacitor CL is 0A once the VCL waveform has settled.

I

_{SW (ave )}

= I

RL( ave)

+ I

CL(ave)

PW

T

× I

S

=

V

_in

+

0, 5

∆V

_C L

R

_L

+ 0 ≈

V

_in

R

_L

if V

in

〉〉 ∆V

CL L R I_SW TIMER I_S i n V L C 0 A ave

F

out

=

1

T

_out

≈

V

in

I

_S

R

_L

× PW

=

V

in

× R

S

V

_ref

R

_L

× Ln(3) × R

T

C

T

=

V

in

× R

S

2,09

× R

L

× R

T

C

T

∆V

L

= PW × m

+

= PW ×

I

S

−V

in

R

L

C

_L











 = SW × m

−

_{= T − PW}

₍

₎

_×

V

in

R

_L

C

_L













NOTE: To obtain good linearity at low values of Vin, the ripple voltage ∆VL must be very small which means that

the time constant RLCL must be very large and this makes the converter very slow to react to changes of Vin.

When ripple is very small, the frequency of the V to F depends on a very small signal easily corruptible with noise or spurious signals which may result in an erratic O/P frequency.

For small values of V_in, the equation derived for F_out is not accurate because ripple must be factored in and Fout becomes a non-linear function of Vin.

Basic V-F Converter L M 3 3 1 in thr Ire Isw RC out Vcc gnd 8 4 1 5 3 7 6 2 Vi n Vcc Fout R_T C_T R_L C_L R_S R_BAL C_in R_P R_HYS C_BY L M 3 3 1 in thr Ire Isw RC out Vcc gnd 8 4 1 5 3 7 6 2 Vi n Fout 0 , 1 µ F 0 , 1 µ F 0 , 0 1 µ F +1 5 V 6 , 8 K 1 0 K 1 0 0 K 4 7 1 µ F 1 2 K 5 K 1 0 0 K _{1 0 Hz} t o 1 0 kHz +1 0 mV t o +1 0 V Fmax adj ust From

F

out

=

V

in

× RS

2,09

_{× RL}

_{× R}

_T

C

_T we find that Rs = 14212 will produce a 10 kHz full scale output given the

standard values on the diagram. The 5k pot will have to be adjusted to some other value because of component tolerance.

PW = 1,1 RTCT = 1,1*6800*0,01µ = 74,8 µs fixed Is = 1,89V/14212Ω = 133 µA

For F = 10 Hz to 10 kHz, duty Cycle = 74,8µ/(0,1 to 100µ) * 100 = 0,0748% to 74,8%

NOTE: PW and duty cycle refer to the switched current source Isw(pin#1). The duty cycle of the output waveform

is inverted, that is D/Cout = 99,925% to 25,2%. Vo+ ≈ +15V and Vo- ≈ 0V

Ripple Voltage

∆V

L

= PW × m

+

_{= PW ×}

I

C

C

_L

= 74,8µ ×

133

_{µ − 10m → 10}

(

)

100k

1

_µ











= 9,94m → 2,47mV

pp

NOTE: Those small ripple values make the V to F vulnerable to noise and unreliable operation may result.

At 10 Hz the discharge of CL is not linear (it is exponential) because RLCL = 0,1s = T ≈ SW.

The speed of the V-F converter is determine by the time constant RLCL. For the above circuit, the rise time of Vthr

is : tr = 0,35/(Fc) = 0,35* 2π*RLCL = 0,22s which is rather slow.

For a faster response of Vthr (and Fout) RLCL should be made smaller but this will entail more ripple voltage

across CL and therefore less accuracy at low Vin and Fout values.

Hysteresis

The amount of hysteresis of the input comparator, for clean and faster switching (no crossover oscillations), is ∆VHYS = IsRHYS = 133µ * 47 = 6,25 mV - this will impair low Vin operation.

Choice of RinCin

The input RC low-pass filter produces a cutoff frequency of Fc = (2π*100k*0,1µ)-1 = 15,9 Hz.

It is used to filter down any HF noise that contaminates the DC input voltage. If the input DC voltage is changed abruptly to a new value, the LM331 input (Vin at pin 7) will settle to its new value in about 5RinCin=5*100K*0,1µ =

50 ms. Therefore the response time of the output frequency will the compounded value of t_r of V_in + t_r of V_thr.

Choice of RTCT

Maximum duty cycle (PW/T)*100 = 1,1 RTCT * Fmax < 95% and should leave enough time for the internal circuit to

reset when SW = T-PW becomes very small. PW should not be too small either.

Choice of RLCL

Select R_LC_L for desired maximum ripple

∆V

_L

= PW ×

I

S

− V

in

R

L

C

_L











 = T − PW

(

)

×

V

in

R

_L

C

_L













and for desired rise time of V_thr : t_r = 0,35*2π*RLCL

Waveforms showing effect of hysteresis provided by RHYS on V6 waveform. When Vin is detected by

the comparator, V₆ pulls up abruptly to prevent oscillations (chattering) at the internal comparator output.

∆VCL VRHYS V₆ V_in HYST IMPROVED V to F CONVERTER L M 3 3 1 in thr Ire Isw RC out Vcc gnd 8 4 1 5 3 7 6 2 A1 +1 5 V I NTEGRATOR V t o F CONVERTER Vo1 I sw I s 0 A av e R_E CF R_p R_T C_T Rs Ps F_out V_in1 I_E -ve

The above converter has a very linear V to F characteristic because its output frequency is totally independant of the ripple voltage present at Vin (pin 7) of the LM331. For fast and reliable operation of the V to F converter, CF

can be made very small in order to get subtantial ripple - 1Vpp recommended

Converter equations

I

_SW

= I

S

×

PW T

= I

E

+ I

CFave

= I

E

= −

V

_in

R

_E

I

_S

_×

PW T

=

−V

in

R

_E

⇒

V

_ref

R

_S

+ P

S

× Ln(3) × RT

C

_T

_{× F}

_out

₌

−V

in

R

_E

F

_out

₌

1

T

=

−V

in

× R

(

S

+ P

S

)

V

_ref

R

_E

× Ln(3) × R

T

C

T

=

−V

in

× R

(

S

+ P

S

)

R

_E

× 1.89 ×1.1 × R

T

C

T

∆V

in

=

I

_E

C

_F

× T − PW

(

)

=

I

_sw

− I

E

(

)

C

_F

× PW

The basic waveforms are shown below.

V

_thr

V

_thr

- 0,5

∆

V

_in

∆

V

_in

V

_in

I

_sw

Vout

0A

0V

15V

I

_S

m+= I

_E

/C

_F

_{m- = -(I sw -I}

_E

)/C

_F

PW = R

_T

C

_T

Ln(3)

The output frequency can be made to respond very rapidly to an abrupt change in Vin by selecting a small value

BASIC F TO V CONVERTER L M 3 3 1 in thr Ire Isw RC out Vcc gnd 8 4 1 5 3 7 6 2 ₊ Vi n +1 5 V 6 , 8 K 1 2 K 5 K 1 0 Hz t o 1 0 kHz +1 0 mV t o +1 0 V 0 , 1 µ F Vmax adj ust 0 , 0 1 µ F 1 0 k 1 0 k 1 0 k 1 5 k 4 7 0 pF 3 k 1 0 0 k 1 0 0 k 0 , 1 µ F 0 , 1 µ F Vout IC SUPPLY BY- PA SS CA P DC OUTPUT

V

_in

V

_in(IC)

SET

V

_CT

RESET

I

_SW

V

_C1

V

_C2

V

THR 0V +5V +9V +7,5V +12,5V +2,5V +10V 0V 0A

V

_REF

R

_S

PW

SET

PW

T

V

_OUT (DC)

The DC output voltage is :

V

_{out (ave)}

= ISW (ave )

× RL

= IS

PW Tin

( )

× RL

=

V

ref

R

S

×

1, 1

R

_T

C

_T

F

_in

× RL

=

2,09

× RT

C

T

F

in

× RL

R

S

The output ripple voltage is given by - see appendix for derivation:

∆V

out (pp )

=

I

_S

R

_L

8

×

PW

R

L

C

L













2

×

1

F

× PW

−1









for F

>

(10

π

RLCL)-1 The output filter has the following TF:

F(S)

=

1

R

2

_C

2

_S

2

_{+ 3RCS +1}

=

R

2

_C

2

(

)

−1

S

2

₊

3

RC

S

+

1

R

2

_C

2

=

R

2

_C

2

(

)

−1

S

+

0,382

RC







 ×





S

+

2,618

RC





The above TF allows us to determine the rise and fall times of V_out in response to an input frequency jump. The approximate value can be determined from the first cutoff frequency:

t

_r

= t

f

≈

0.35

F

_C1

=

0.35

0.382

2

_{π RC}











= 5.757 × RC

The internal latch SET pulsewidth (PWset) must be less than the current pulsewidth PWT = 1,1 RTCT , otherwise

the circuit will not work properly. PWset is determined by the input coupling capacitor and the input resistance

10K 10K

.

PW

_SET

= R

in

C

in

× Ln

V

1

− V

F

V

₂

_{− VF}











 = 5K × 470 p × Ln

12.5

₉

− 7.5

− 7.5







 =

2.83

µs

PW

T

= 1,1 × RT

C

T

=1,1 × 6.8K × 0.01µ = 74.8 µs

NOTE: PW_set = 2.83 µs may not be long enough to set the internal RS latch - minimum time not specified.

NOTE: If the input square wave has a large amplitude, the protection diodes will turn on and the exponential

pulses at the junction of the two 10K resistors will have two time constants, that is:

10K 10K

+ 3K

(

)

× 470 p

when one of the diodes is ON (

10K 10K

) x 470p when the diodes are OFF.

APPENDIX 1 Derivation Of Output Ripple Voltage R1 _C1 R 2 C2

I

SW R1 C1 R 2 C2

V

_C1

V

_C2

V

C1

V

C2

N O RTO N

THEVENIN

V

_{T H}

I

_SW

R

₁

V

T H

V

_{C 1}

V

C 2 0V

PW

T

_V

O U T(D C )

V

_{O U T}(D C )

I

SW

R

1

∆V

C1(PP)

=

1

R

₁

C

₁

V

TH ( AC)

dt

t1 t2

∫

=

_R

1

1

C

1

× PW × I

(

S

R

1

− V

ave

)

=

1

R

₁

C

₁

× PW × I

(

S

R

1

− I

S

R

1

( )

PW_T

)

∆V

C1(PP)

=

1

R

₁

C

₁

× PW × I

S

R

1

1

−

PW T

( )

(

)

=

1

R

₁

C

₁

× PW

2

_{× I}

S

R

1

( )

_PW1 −1_T

∆V

C2(PP)

=

1

R

₂

C

₂

V

C1(AC )

dt

t1 t2

∫

=

1

R

₁

C

₁

×

1 2

× ∆V

C1( PP)

×

T 2

×

1 2

(

)

=

1

R

₁

C

₁

× ∆V

C1(PP)

×

T 8

(

)

∆V

C2(PP)

=

1

R

₁

C

₁

×

T

8

×

1

R

₁

C

₁

× PW

2

_{× I}

S

R

1

( )

_PW1 −_T1











 =

I

S

R

1

8

×

PW

R

₁

C

₁













2

×



_

_PW

T

−1



_

NOTE: R₁C₁ = R₂C₂