Electrodes in Biomedical Instrumentation

Electrodes are devices which are used to convert ionic voltages into electronic voltages. Two electrodes can be used as a transducer.

Electrode Paste: Electrode Paste is an electrically conducting material employed as an interface between the electrode and surface of the body.

Types of Electrodes in Biomedical Instrumentation:

A wide variety of electrodes can be used to measure bio-electric events, but nearly all can be classified as belonging to one of the three basic types.

(a) Microelectrodes
(b) Skin surface electrodes
(c ) Needle electrodes

(a) MICRO ELECTRODES : 

Electrodes which are used to measure bio electric potentials near or within a single cell are called micro electrodes.

Microelectrodes are generally of two types. (i) Metal electrode (ii) Micropipette

i) Metal electrodes

Metal electrodes are formed by electrolytic ally etching the tip of a fine tungsten or stainless steel wire to the desired size. Then the wire is almost coated to the tip with an insulating material. Fig shows a commercial type of metal electrode.

ii) Micropipette

The micropipette type of microelectrode is a glass micropipette with the tip drawn out to the desired size (usually about 1 micron (1μm) in diameter.) The micropipette is filled with an electrolyte compatible with the cellular fluids. A commercial type of microelectrode is shown in fig. In this electrode, a thin film of precious metal is bonded to the outside of a drawn glass electrode. All the above types of micro electrodes are used to take measurement within the cell or near the cell.

(b) SKIN SURFACE ELECTRODES: 

Electrodes which are used to measure ECG, EEG and EMG potentials from the surface of the skin are called skin surface electrodes.

The larger electrodes are usually associated with ECG where as smaller electrodes are used in EEG and EMG measurements. Following are various types of surface electrodes.

(i) Metal plate electrodes. (Limb electrodes)
(ii) Suction cup electrodes. (chest electrodes)
(iii) Adhesive tape electrodes.
(iv) Floating electrodes.
(v) Disposable electrodes.
(vi) Ear clip electrodes.

(i) Metal plate electrodes. (Limb electrodes)

The most common type of electrodes routinely used for recording ECG are rectangular or circular surface (metal plate) electrodes. The material used is German silver, nickel silver or nickel plated steel. They are applied to the surface of the body with electrode jelly. The electrodes are held in position by elastic straps. They are also called limb electrodes as they are most suitable for application on the four limbs of the body. They are reusable and last several years. These are generally preferred for use during surgery and are not suitable for use in long term patient monitoring.

(ii) Suction cup electrodes

Suction cup electrode is commonly used to record the uni- polar chest leads. The electrode is popular for its practicality, being easily attachable to fleshy parts of the body. Electrode jelly forms the vacuum seal. This electrode suffers by electrode slippage or movement after a sufficient length of time.

(iii) Adhesive tape electrode (Pre-jelled electrodes)

The adhesive tape electrodes reduce movement artifact by limiting electrode movement and reducing interface impedance. The pressure of the surface electrode against the skin may squeeze the electrode paste out. To avoid this problem, adhesive tape electrode is used.It consists of a light weight adhesive metallic screen backed by a pad for electrode paste. The adhesive backing holds the electrode in place.

(iv)Floating electrodes

The principle of this electrode is to practically eliminate movement artifact by avoiding any direct contact of the metal with the skin.

The floating electrode consists of a rigid plastic cup which contains the metal electrode and holds the electrode jelly. These are generally attached to the skin by means of two sided adhesive rings which adhere to both the plastic surface of the electrode and the skin. During long term monitoring or exercise testing this electrode is an important part of the system.

(v) Disposable electrodes

Various types of disposable electrodes have been introduced in recent years to eliminate the requirement for cleaning and care after each use. In general Disposable electrodes are of the floating type with simple snap connectors by which the leads, which are reusable, are attached.

(vi) Ear clip electrodes

A special ear clip electrode was developed for use as a reference electrode for EEG measurement.

(c) NEEDLE ELECTRODES

Electrodes for electromyography work are usually of the needle type. Needle electrodes are used in clinical electromyography, neurography and other electrophysiological investigations of the muscle tissues underneath the skin and in the deeper tissues. The material of the needle electrode is generally stainless steel.

Needle electrodes are of various types. Some are,
(i) Monopolar
(ii) Bipolar.

(i) Monopolar needle electrode

The monopolar needle electrode usually consists of a Teflon coated stainless steel wire which is bare only at the tip.

(ii) Bipolar needle electrode

A concentric (coaxial) needle electrode contains both the active and reference electrode within the same structure. It consists of an insulated wire contained within a hypodermic needle. The inner wire is exposed at the tip and this forms one electrode. This needle electrode looks like a medicine dropper. Some electro-encephalography use small sub dermal needles to penetrate the scalp for EEG measurement. They are not inserted into the brain. They merely penetrate the skin.

Characteristics of DC Compound Motor

Characteristics of D.C. Compound Motor:

Electrical Characteristics :

The torque equation for d.c. compound motor is

T = K₁ΦI_a = K₁[Φ_sh + Φ_se] l_a

With increase in armature current Φ_se increases and consequently the torque. If the shunt field is more stronger than the series field the torque current characteristics approaches as that of d.c. shunt motor. And in case series field is stronger than the shunt field, the torque current characteristics approaches as that of d.c. series motor. The comparison curves are drawn in Fig.

In the case of differential compound motors since series field opposes the shunt field, the net flux decreases as load is applied to the motor; the result is, there is a decrease in the rate at which the motor torque increase with load. Therefore, such motors are not in common use. Another draw-back is, weakening of flux with increase in load, there is a tendency of speed unstability.

Speed and Armature Current Characteristics :

For the long shunt compound motor

V = E_b + I_a (R_a + R_se)

and E_b = K₁ΦN = K₁[Φ_sh + Φ_se]N

Where Φ_sh and Φ_se are flux due to I_sh and I_se

N = E_b / K₁[Φ_sh - Φ_se] =   V - I_a(R_a + R_se) / K₁[Φ_sh + Φ_se]

With the increase in l_a, Φ_se increases and V - I_a(R_a + R_se) decreases, Thus with the increase in I_a, the speed drops at faster rate in cumulative compound motor than in shunt motor. If the shunt field is stronger than series field, the curve tends to shunt motor and if the series field is stronger than shunt field, it tends to series field curve. The comparison characteristic is shown in Fig.

Speed-Torque Characteristics :

The torque in d.c. compound motor is given by

T_a = K₁ [Φ_sh + Φ_se] l_a

Or I_a = T_a/ K₁[Φ_sh + Φ_se]

But N = V - I_a(R_a + R_se) / K₁[Φ_sh + Φ_se]

N = (V/ K₁[Φ_sh + Φ_se] ) - ( I_a(R_a + R_se) / K₁[Φ_sh + Φ_se])

Substituting the value of I_a

N = (V/ K₁[Φ_sh + Φ_se] ) - ( T_a(R_a + R_se) / K₂[Φ_sh + Φ_se]²)

It is seen that an increase in torque increases the armature current and so also the flux, decreasing the speed rapidly. The decrease is more predominant than that compared with d.c. shunt motor. Therefore, the speed torque characteristics approaches the shunt motor characteristics if the shunt field is stronger. In case series flux is stronger than the shunt flux, the speed torque characteristics approaches the series motor characteristics. Depending upon the relative strength of shunt and series field the speed torque can occupy any position between the curve 1 and 2 in Fig.

Characteristics of DC Series Motor

1. Electrical Characteristics :

In a d.c. series motor, the armature current and series field current are same and therefore Φ ∝ I_a. The armature torque is equal to

T_a ∝ Φ I_a or

T_a ∝ I_a²

This is true till the point of magnetic saturation. When I_a is zero, torque is also zero and when I is small torque is also small. Since is proportional to square of the armature current the curve is parabolic. After saturation Φ is almost constant and for any increase in armature current torque increases linearly i.e., T_a ∝ I_a. The shaft torque is less than armature torque by rotational losses, The curve is shown in Fig.

2. Speed and Armature Current Characteristics :

For a d.c. series motor

E_b = V - I_a (R_a +R_se) and E_b = ΦN x ZP/60A

or E_b = K_aΦN

Where K_a = ZP/60A

Substituting the values,

K_aΦN = V - I_a (R_a +R_se)

or N = V - I_a (R_a +R_se)/ K_aΦ

or N = V/ K_aΦ - I_a (R_a +R_se)/ K_aΦ

But for a dc series motor, Φ ∝ I_a, therefore

N = V/ K_bI_a – (R_a +R_se)/ K_b ; where K_b = I_a/K_a

From the above equation, it is seen that neglecting armature reaction and with saturation the speed-current characteristics of d.c. series motor is hyperbolic as shown in Fig. When l_a increases Φ also increase but due to demagnetisation effect of armature reaction and saturation, the air gap flux tends to remain constant and for constant flux Φ the term V/K_aΦ remains constant and the term l_a [R_a + R_se]/ K_aΦ increases with armature current linearly.

Thus for larger values of armature current, the curve takes a straight line path. At no load the armature current is small and so the armature drop I_a (R_a + R_se) and can be considered negligible as compared to terminal voltage.

Then N = V/K_aΦ, But Φ ∝ I_a,therefore N = V/K_bl_a

On no load when the armature current tends to zero, the speed tends to infinity. Therefore, the no load speed of d.c. series motor is dangerously high and due to this reason the d.c. series motor must not be started without a load. The curve is shown in Fig.

3. Speed-Torque Characteristics :

The torque of d.c. series motor is proportional to the square of armature current i.e.

I_a² ∝ T_a or

I_a ∝ √T_a

Neglecting the armature reaction and saturation

N = V/K_bI_a  or  N = V/K_b√T_a

Squaring both sides

N² =  V²/K_cT_a 

or T_a  = V²/N²K_c 

or T_a ∝ 1/N²

The speed torque characteristics is also hyperbolic in nature. But with saturation and armature reaction large torque requires larger currents and these large currents tends to make the air gap flux constant and the effect is T_a ∝ I_a instead of T_a ∝ I_a². The curves approaches straight line as shown in Fig.

Characteristics of DC Shunt Motor

CHARACTERISTICS OF DC MOTORS:

The characteristics curves of d.c. motor are curves drawn to show the relation between armature current, speed and torque. The following are the general characteristics of interest in a d.c. motor.

a. Electrical characteristics : This shows a relation between torque developed and armature current in a d.c. motor.

b. Speed and armature current characteristics : This shows the relation as to how the speed varies with armature current.

c. Speed-Torque characteristics : This is also mechanical characteristics. It gives the relation between speed and torque in a d.c. motor.

Characteristics of D.C. Shunt Motor

1. Electrical Characteristics :

In a d.c. shunt motor, shunt field flux is dependent on terminal voltage V and the shunt field resistance. Assuming that the terminal voltage is constant, the shunt field flux is also constant i.e., Φ is constant, then

Torque developed is given by = E_bI_a/ω

Torque developed in armature = 0.159 [ΦZl_a] P/A = I_aK₁

Where K₁ = 0.159 x ZΦP/A is a constant.

The torque developed in armature (T_a) ∝ I_a.

It is a linear relation and practically a straight line front the origin. Since shaft torque is equal to the armature torque minus the rotational losses, the shaft torque line also follows the armature torque line as shown in dotted in Fig.

2. Speed and Armature Current Characteristics:

For a dc shunt motor assuming that flux remaining constant

E_b = V – I_aR_a = ZΦNP/60A

Or V – I_aR_a = N x ZΦP/60A = K₂N

Where, K₂ = ZΦP/60A

Or V – I_aR_a = K₂N

The terminal voltage V and armature resistance are constant. If I_a = 0, then N is maximum and as I_a increases N decreases. As la increases, load on the shaft also increases. Invariably the speed of the shunt motor decreases with the increase of load as shown in Fig.

3. Speed-Torque Characteristics :

In a d.c. shunt motor T_a ∝ I_a and V - l_aR_a = K₂N

From these two equations, it is evident that as torque increases the armature current also increases proportionately and the net value of the back e.m.f. decreases. Decrease in back will result in decrease in speed. Hence, when speed is zero, back e.m.f. is zero, armature current is also zero and torque is maximum. The curve is shown in Fig. As speed increases armature current decreases to minimum but does not become zero and torque decrease. Therefore the characteristics line does not follow the speed axis.

Voltage and Speed Relation in DC Motor

VOLTAGE EQUATION OF DC MOTORS

1. DC Shunt Motor:

In a dc shunt motor, the field winding is connected across the armature and the supply is given to the armature. As such the current for the field winding is taken from the supply. The armature current is therefore equal to the difference of line current and the shunt field current. Therefore,

I_a – I_L - I_sh

I_sh = V/R_sh

E_b = V – I_aR_a

Where,

I_sh is the shunt field current

R_sh is the shunt field resistance.

2. Back e.m.f. in DC Series Motor:

In a D.C. series motor, the applied voltage V has to supply the ohmic drop in armature (I_aR_a) and also series field voltage drop (I_seR_se) ie.,

V = E_b + I_aR_a + I_seR_se

Since the field winding is in series with the armature, the current in the armature and series field are same. Therefore,

I_L = I_a = I_se

Voltage equation can be rewritten as under,

V = E_b + I_a(R_a + R_se)

Where,

V is the applied voltage in volts

I_a(R_a + R_se) is the voltage drop in the armature and series field winding.

Multiplying both sides by I_a

VI_a = I_aE_b + I_a²R_a + I_a²R_se

is the power equation

Where

VI_a is the power input in watts

I_aE_b is the electrical equivalent of mechanical power developed

I_a²R_a is the copper loss in the armature

I_a²R_se is the copper loss in the series field winding

3. Back emf in DC Compound motor:

In DC Compound motor there are two possible connections. One when the shunt winding is connected parallel to the armature, it is called short shunt compound motor and when the shunt winding is connected parallel to the supply, it is called long shunt compound motor. The two types of connections are shown in figure.

In the long shunt compound motor, the voltage equation of the armature circuit is given by,

V = E_b + I_aR_a + I_seR_se

But, I_a = I_se

Therefore, V = E_b + I_a(R_a + R_se)

And the current equation is I_L = I_sh + I_a

Multiplying the voltage equation both sides by I_a

I_aV = I_aE_b + I_a²R_a + I_a²R_se

Where I_aV is the power input to the armature circuit. The total power taken by the motor is equal to the sum of the power input to armature circuit and shunt field circuit. That is,

I_LV = I_aV + I_shV

The electrical power equivalent to mechanical is I_aE_b.

In the short shunt compound generator, the voltage equation is given by,

V = E_b + I_aR_a + I_seR_se

And, I_L = I_se = I_a + I_sh

Where, I_L = Line current in amps

I_a = Armature current in amps

I_sh = Shunt field current in amps

= V_sh/R_sh = E_b – I_aR_a/R_sh

The electrical power develop equivalent to mechanical is IaEb. In all the cases the back emf is also equal to,

E_b = ZΦNP/60A

SPEED EQUATION OF DC MOTOR:

The speed equation of dc motors can be deduced from the voltage equation itself. Thus we can find the voltage and speed relation in dc motor. The back emf equation for a motor is given by,

Eb = V – IaRa

But, Eb = ZΦNP/60A

or Eb = K1ΦN where, K1 = ZP/60A

or Eb ∝ ΦN or N ∝ Eb/Φ

That is, N ∝ (V – IaRa)/Φ

From the above it is seen that for the speed to change either

a. the field flux has to be changed or

b. the armature current has to be changed. Change of armature current means change of load conditions.

For a dc series motor,

N ∝ (V – Ia(Ra + Rse))/ Φ

It should be noted that for the field flux to change, a resistance called the diverter is added in parallel to the series field and for the armature current to change a resistance is connected in series to the series field.

Torque in DC Motor Formula

Torque in DC Motor with Formula

Turning or twisting moment of a force about the axis is called torque in DC Motor. The unit of torque is Newton-metre. It is measured by the product of the force and the radius at which this force acts. Consider a pulley of radius R metres acted upon by a force on the circumference with F Newtons to cause the pulley to rotate at a speed of N rev. per second as shown in Figure.

Then as per the definition torque = F x r Newton-metre

Work done by this force in one revolution (Force x distance) = F x 2πr Joules

If N is the speed in r.p.s. then Work done/second = F x 2πr x N = (F.r) x 2πN

2πN is called the angular velocity and is represented by ‘ω'. It is measured in radians/second.

Power developed (P_m) = Two Joules/second or watts

The torque developed at the shaft in DC Motor is always lesser than the torque developed at the armature because of losses.

The formula of torque developed by the armature = T_a.2πN watts

The mechanical power developed in the armature =, E_b l_a watts

But the mechanical power developed in the armature is equal to the armature torque i.e.,

E_bl_a = T_a.2πN/60 where N is in r.p.m. and

N_rpm/60 = N_rps

But E_b = ZΦNP/60A

Substituting for E_b

ZΦNP/60A x l_a = T_a.2πN/60 or

T_a = ZΦ l_a/2π x P/A

= 1/2π Φ Zl_a x P/A = 0.159 Φ Zl_a [P/A] N-m

= 0.159/9.81 x Φ Zl_a x P/A kg-m

= 0.0162 Φ Zl_a x [P/A] kg-m

This is also known as the gross torque. The torque developed at the shaft is the useful torque and is known as shaft torque (T_sh).

BHP (metric) = Tshaft x 2πN/735.5 where N is in r.p.s.

Or T_sh = (BHP)_m x 735.5/2πN

The motor output is given by T_sh x 2πN watt

T_sh = output in watts/2πN  , where N is in r.p.s.

= 60/2π x Output/N = 9.55 x Output/N  N-m

Where N is in r.p.m

The difference between armature torque and shaft torque is the torque lost.

Torque lost = 0.159 x iron and frictional loss/N  N-m

Case 1 Shunt Motor:

The flux is constant in shunt motor and is dependent on the terminal voltage and shunt field resistance. Therefore,

T_a ∝ I_a

Case 2 Series Motor:

In the case of a series motor the armature and series field currents are same i.e., I_a = I_se = I_L, therefore

Φ ∝ I_a and T_a ∝ I_a²

and also the torque in dc motor formula,

T_a = E_bI_a/2πN = 0.159 E_bI_a/N  N-m

= 0.0162 E_bI_a/N kg-m

= 0.0162/N x Power developed in armature Kg-m

Difference between Developed Torque, Useful Torque and Lost Torque

The whole of the armature torque is not available for doing any useful work because a certain percentage of it is required for supplying iron and frictional losses in the motor. Therefore, the net torque available is the shaft torque. The difference between the armature torque and shaft torque is the torque lost. The torque developed in the armature is called gross torque and the torque which is available at the shaft which is much less than the torque developed in the armature is called shaft torque or useful torque.

Significance of Back EMF in DC Motor

Significance of Back EMF in a DC Motor

As soon as the armature starts rotating inside a magnetic field due to the current in the conductor, the following conditions are set in

a. The conductor is in motion

b. The flux of the main pole exists

c. While the conductor is in motion, it also cuts the main pole flux

This condition creates a situation for inducing e.m.f. in the conductor. The direction of induced e.m.f. as found by the Fleming's Right hand rule, is in direct opposition to the applied voltage across the armature conductor. It is therefore termed as back e.m.f. (Eb). The magnitude of back e.m.f. (back emf in dc motor formula) is given by :

E_b = ZΦNP / 60A

Where,

Z is the number of conductors in the armature

Φ is the flux of the main pole in Webers

N is the speed of rotation of the shaft in r.p.m

P is the number of poles of the machine

A is the number of parallel path of the winding

A = P for Lap winding

A = 2 for Wave winding

This back e.m.f. acts in opposite direction to the applied voltage in the armature as shown in Figure. Hence, the net voltage across the armature would be the difference between the applied voltage and back e.m.f.

i.e., Net voltage across armature = (V — E_b) Volts

Where,

V is the applied voltage across the armature

E_b is the back e.m.f.

If the resistance of the armature is R_a, then the armature current is given by

Armature current = Net voltage across armature /Armature resistance

I_a =(V – E_b)/ R_a amperes

It should be remembered that the magnitude of back e.m.f. is dependent upon the speed of rotation of the shaft (N). If the speed is zero, the back e.m.f. is also zero and as the speed increases the magnitude of back e.m.f, also increases. At stand still or starting position, the shaft is stationary and therefore the back e.m.f. is zero. Rewriting the equation for applied voltage

l_aR_a = V—E_b or

V= E_b +I_aR_a

The voltage V applied across the armature has to

a. overcome the back e.m.f. E_b and

b. supply the armature ohmic drop l_aR_a

This is known as the voltage equation of d.c. motor. Multiplying the equation on both sides by l_aR_a, power equation is obtained.

Power = VI_a = E_bI_a + l_a²R_a

Where,

VI_a is the electrical input to the armature

E_bl_a is the electrical equivalent of mechanical power developed in the armature

I_a²R_a is the copper loss in the armature

Hence, it would be seen that some power is wasted in the armature out of the input and the rest only is converted into mechanical power within the armature. The gross mechanical power developed by the motor is given by

P_m = VI_a— I_a²R_a

Differentiating both sides with respect to l_a and equating the result to zero,

dP_m/dI_a = V — 2I_aR_a =0

Therefore

I_aR_a = V/2

Thus, the gross mechanical power developed by the d.c. motor will be maximum when the back e.m.f. is equal to the half of the applied voltage. If this condition is taken into account, then half the input would be wasted in the form of heat and taking into other losses like frictional and magnetic losses, the motor efficiency would fall to 50%. As such this condition is not realised in practice.